I'm working with canon CR2 RAW files. My images usually have 30MB when I import into Lightroom, but when I bring into Photoshop for an adjustment and get back to Lightroom the TIFF file generated is huge. I'm shooting with a 750D, and I have a file with 28.3 MB, after generating the TIFF (single layer) the TIFF file has now 137MB. I usually put all of my Lightroom images and library in the cloud, but I think I'll run out of space pretty soon with files like this. Is there a way to get compressed or smaller TIFF files?
If you really want to decrease the TIFF size, you should be looking at lossy compression. A good question is, why do you want to use TIFF and why not JPG in the first place? However, lossy compression isn't good if you plan to edit the file later, so I understand the desire to use TIFF.
Another way is to just store the CR3 RAW file and recreate the TIFF as needed. The TIFF is larger, because a camera has for one pixel just one luminance value (Bayer filter), whereas the TIFF is created after using a demosaicing algorithm that assigns three color values to a pixel (red, green, blue).
A TIFF has no way to specify raw data and what demosaicing algorithm to run on the raw data. Therefore, the TIFF will be larger.
What I do is that I just store the CR2 files (my camera has CR2 format and not CR3 format).
Apparently TIFF supports lossless deflate compression, but even that would reduce the file size barely by tens of percent. A better option is to just stick with the CR3 format.
Some RAW software supports storing the instructions for creating the TIFF into a separate file (non-destructive editing). At least the software I use, darktable (open source software), supports such non-destructive editing and storing the instructions for creating the TIFF into a file.
I'm putting this in as an answer just because it's too much for a comment... yet doesn't really answer the question, so bear with me a bit & be kind with the downvotes ;)
In accordance with Please put your answers in the answers section, even if they're short
I use a different workflow, camera & software [which is why this isn't a real answer]
I do my initial RAW work in Nikon's ViewNX-i. This stores a sidecar file of what adjustments have been made to the RAW for display.
I then export this tweaked version as TIF if I need to work in Photoshop. This often results in a lot of layering, masking etc & so is best saved as an actual PSD file.
I then trash the intermediate TIF. It has served its purpose & if I ever need it back, ViewNX-i still has the tiny sidecar file to recreate it in seconds.
You must be using 16 bit TIFF files? But 16 bit TIF seems overkill, since you've surely already done the extreme shifts of gamma and white balance while it was raw. I would suggest 8 bit TIF with LZW compression.
TIF does offer LZW compression, which is a little less effective in 16 bits vs 8 bits. But while not dramatic size reduction like JPG, LZW is lossless, unlike JPG. Lossless meaning no JPG artifacts are added.
The 750D says 24.2 megapixels.
24.2 megapixels and 12 bit raw is about 35 MB files, if uncompressed. And there is a little overhead, like the Exif data and an embedded JPG image too.
16 bit TIF is six bytes per pixel, uncompressed. 24.2 million x 6 = 145 million bytes (138 MB).
8 bit TIF files are three bytes per pixel. 24.2 million x 3 = 72.6 million bytes (69 MB).
That is simply how large the data is. It is a big image.
If you do use JPG, it is 8 bits. And use only HIGH JPG Quality for it to minimize JPG losses.