I'm shooting in Manual on bright, sunny day. ... Settings: 1/200 SS, f2.8, ISO 125.
Did you look at your meter? It was likely telling you that you were overexposed. Purely on the ambient. If you were shooting in sunny-16 conditions, with these settings, you'd be overexposed by four stops even without the flash. Throw the flash in, and you're overexposed by even more.
With fill flash, you're typically going for settings a stop or two lower than what you'd use for ambient, and then adding in flash to make your subject pop against a darker background.
I want to maintain f2.8 to blur background.
And you've just discovered why off-camera flash shooters will pay more to have HSS capability in their radio triggers and flashes. So they can shoot in bright light with thin depth of field and use a flash. This is one of the main drawbacks to having a cheapie manual-only flash setup that can't do TTL/HSS.
What am I doing wrong?
You're assuming you can use f/2.8 and 1/200s and get good exposure in bright sunlight. :) The problem is that with a manual flash like a YN-560, the 1/200s is a definite hard limit and your ISO is already as low as you can go. So to use f/2.8 you'll have to use some additional gear.
The easiest low-cost fix is to get neutral density (ND) filters for your camera lens. ND filters are like sunglasses for your lens. In this case, you probably need a four-stop or six-stop filter. This will bring the exposure back down into reasonable range, and still allow you to use a wider aperture setting with an 1/200s shutter speed.
You could also get a radio triggering setup that allows for HSS; e.g., a Godox X1T transmitter and a TT600, or a YN-685 and YN-622-TX. But HSS is also a game of diminishing returns—you lose more power than if you used an ND filter setup. But, OTOH, you actually get a faster shutter speed, so if you need to freeze action with a faster shutter speed, HSS will actually work, where an ND filter won't.