The commenters so far (Dan Wolfgang, Itai and jrista) are right, at least in as far as you aren't going to find something that hits all of your requirements at anywhere near your price point — unless you can find the used-equipment bargain of the century, a new and unheralded high-quality product from an emerging economy, or an honest crook selling actual carbon fiber Gitzos that "fell off the truck" in your local mall parking lot. Heck, what a lot of photographers would call "a good ball head", something with silky-smooth action, a gorilla-like grip when clamped, separately-adjustable drag, a huge range of movement and independent panning will send you over both your price and weight limits all by itself, and you're still hand-holding (but now with a four-pound ball head stuck to the bottom of your camera).
You're going to have to settle for a compromise, and the trick is in finding something that compromises the fewest points on the checklist by as little as possible. It isn't easy.
You want something reasonably tall, but that collapses to a small package. That's going to mean a lot of leg segments, and the thinnest ones are going to be pretty thin. The lighter you make the tripod, the thinner the tubes (both in diameter and wall thickness) are going to be. If you go too light, the tubes will be thin enough that sturdiness is impossible at full height, and while you can remember to extend the tubes in widest-to-narrowest order as needed, it makes no sense to have any leg segments that really can't be used at all. The expensive option is to use a super-lightweight material (carbon fibre and basalt are common enough), but at this point you're kissing your budget a fond farewell, knowing you'll never return. Or you can compromise on the weight requirement just a bit. Or on the extended height, or the collapsed length.
Getting a compact tripod to act tall also means a fairly long center column. That doesn't have to impact all of your photography, since you don't always have to have the tripod at full height, but it will make "danger zone"† photographs nearly impossible at full height (even if you use a damping weight). That also means that there's a lower limit on the height of the tripod. A "trick" center column that acts as a horizontal boom (as on the Manfrotto 190XPROB) or a reversing center column can get around that, but at a cost: the trick columns add weight, and the reversing columns will put your viewfinder at ground level and make the camera controls inaccessible (though you can get around that to a degree with a remote release and live view).
Since getting tall means a lot of adjustable bits, you're going to want to make sure that all of the locks are reasonably strong. Meeting the tripod in person and applying just a little more force than is reasonable (just a little) is the only way to check this out. And a good, long heart-to-heart is really the only way to judge sturdiness and stability as well.
As for the ball head, you're probably going to have to settle for "good enough". At this price point, you're probably looking at something with a bit of a grainy feel, a somewhat limited range of motion (outside of the "vertical" slot) and one lock to rule them all (no separate pan and drag adjustments). You'll notice the graininess most when your camera/lens is at its lightest; it would be really annoying-feeling with a lightweight entry-level body and a kit or pancake lens, for instance, but much less noticeable with a 5D and a 70-200. The limited range of motion is a mechanical necessity; anything more than about ±30-35 degrees of freedom means that the cup and ball have to be larger, the cup needs to be sturdier, or the locking force has to be so weak that it can't support much of a load off-center. The separate drag and pan adjustments are just an added expense — a budgetary concern. What all of this means is that a "good enough" ball head is going to require thoughtful use: you need to be in control of the camera when you release the lock. (With a separate drag adjustment, you can afford to be a little less careful, since it can be adjusted so the the lock is released but you still need to push the camera around to move it.) I'd go a long way out of my way to avoid the "joystick" heads — the center of gravity of the camera is too far from the ball for it to be anything like useful for a heavy camera/lens combo no matter what the load limit looks like on paper.
Now, with all of that said, you can decide on your compromises.
As luck would have it, I've just returned from a similar quest. My requirements were slighly different: I needed a reasonably low price because I'm on a fixed disability pension; light weight because I can no longer hold a camera without a tripod except on rare tremor-free days, and I can't physically manage the load of my "real" tripods anymore (Parkinson's is a bitch); compact folded size because I can't be carrying a four-foot anything absolutely everywhere I go (try it with just a cardboard tube from a roll of paper some time and see how easy life can be); and relative tallness because stooping is far too often a complete no-go for me now. Minimum height wasn't a concern. Sturdiness was — I may be a crip, but I'm still a photographer. (I was just thinking that life would actually be easier once I'm confined to a chair and can have a camera mount built into my cyborg unit.)
What I found on my quest were a whole bunch of things that looked sort of like tripods, but didn't feel much like tripods. Most were wobbly or spindly to the point of being little more than steadiness aids, which is sort of okay if that's what you want. (But if you need to be hands-on all of the time, why not get a monopod? If light tremors on a good day can overpower the 'pod, it's not good enough for me.) Many others were too short to be useful to me, although to someone who isn't handicapped (or who is shorter), that should be much less of a worry. (Don't be afraid to stoop, kneel or sit if you can — it'll really open up your options.) Added features without a corresponding bump in price almost always meant that the basic tripodness of the machine suffered, usually to an unacceptable degree.
What I wound up with was a Benro A2690 "Travel Angel" with a BH-1 head (it comes as a kit with a carry bag, spikes and tools). It's about a half-pound heavier than you want, but since the legs fold back over the column/head, a little more compact when folded than you specced (at just under 18"/45.5cm). It's very conservatively rated for 6kg (my tests have shown that it will hold quite a bit more if you're the type that needs to run with scissors). With the bottom leg segments and the column retracted, it's very sturdy and stable (though only about 45"/114cm tall). With the legs fully extended it's about 55"/140cm (putting the viewfinder at about 59"/150cm) and sturdy/stable/well-damped enough for anything but the most critical long-lens work (luckily, not part of my oeuvre these days). With the center column fully extended, it's still reasonable (I'd want to hand-hold the camera at longer than 300mm for extra damping) and actually too tall for me to use comfortably with the camera horizontal on flat ground (at a platform height of about 63½"/162cm and a viewfider height almost 4"/10cm higher still — I have to stand straight to raise my eye to the viewfinder, and that takes some effort these days). The legs have two stop-angles (independent of each other), but I wouldn't use the wide setting with the bottom segment(s) extended — the tubes are just too thin and there's not enough overlap at the locks to support them. (Having any of the leg segments fully extended on the wide setting is probably not a good idea. The extra overlap helps a lot when the tubes are incompletely extended.) It won't go lower than 16½" (20-20½" at the viewfinder assuming no vertical grip on the camera and a horizontal orientation). The leg and center column locks haven't shown any tendency to slip unless I put way more weight on them than is reasonable. The BH-1 head is horribly grainy-feeling and a one-lock design, but it stays where you put it, which is better than I can say for most heads at or around this price point. All in all, it's not a $1000 tripod with a $500 head, but the compromises it makes are the right ones for me. You'd need to decide for yourself if they're right for you.
Go out if you can, and get hands-on. Good retailers (and we have a couple of excellent ones here in Toronto) are pretty tolerant of weirdo artist types doing non-life-threatening interpretive dances with their display gear. Hands-on is the only way to tell what's right for you. And it'll give you a chance to compare what you can afford to what you want to be able to afford — you'll want to know what the real deal feels like so you can judge the compromises you will inevitably have to make.
ADDENDUM: Shopping around at a good local retailer then buying online for a better price isn't very nice—it costs the retailer good money to let you play with the product. If you want the local retailer to remain available for hands-on, then buy from them. Save the online purchases for the times you don't need the personal touch.
† Any mechanical system will have some resonance, and that applies to a tripod/camera/lens combo as much as to anything else. At high shutter speeds, slight motion/vibration is not going to be a problem. At really long shutter speeds, the motion will have completely damped out before the majority of the exposure occurs. There's a sour spot in the middle, usually between 1/60 and 1/8 of a second depending on the camera, lens and tripod, where the shutter will be open long enough to visibly record the vibration but not long enough to have allowed a solid exposure to outvote the vibrating bits.
