I can't seem to do squats without lifting my heels off the ground, which makes me think I'm doing it wrong and I won't get the results I want. Here's the catch: I've had multiple ankle surgeries on both ankles, so they have a limited range of motion. Other catch: I'm flexible, so that is not the issue.
Oh, and if this would matter, I'm not overweight. 5' 7", 120 lbs and have horrible balance.
When doing squats, your back should remain straight and you shouldn't be bending at the hips. Feet should be shoulder width apart and your center of gravity should be over your heels. The motion is just like sitting down. You should be bending at the knees and making your but go out, not bending over at the hips.
The reason you are most likely standing on your toes is because you are leaning forward and shifting the center of gravity forward with you. Too much weight can lead to bad form like this, especially because your body has a hard time stabilizing the weight. Try also using a spotter, or a squat rack that has tracks for the barbell. That might help you focus more on the squat as opposed to keeping your balance. Invariably you'll give up a bit of the benefits of the exercise, since you'll no longer be using as much of your core for stabilization, but you'll do a much better squat that way.
Assuming when you stand, you stand with your feet flat and not tip-toed, the problem is not your ankle injury. You're not holding the weight appropriately. The weight should be on your heels, and when you drive the weight up, you should be pushing off your heels and driving your back into the bar (if you do it with weights). Almost like trying to push yourself backwards. When you descend you should try visualizing sitting down. Your knees stay in the same spot and your butt squeezes down, rather than your knees folding in to achieve depth.
Currently you're leaning too far forward and rounding your back on the ascent. This allows you to then go on your tip toes, whereas without rounding your back it wouldn't be easy. Your problem should be solved simply by squeezing your back backwards in an arch. And throughout the whole squat, maintaining that back arch. It may also help to take a wider stance.
Your form is just really bad. You need to push your butt back , but at the same time push your chest forward and keep your back as straight as possible (not straight though). You need to feel your weight on top of your heels and make sure your knees are not going over your toes when squatting.
Very easy solution. Put a chair behind you and do your squats and once you feel the chair go back up, so pretend to sit in the chair. Then move on without the chair. Your ankles may or may not be the problem, for instance I had surgeries on both ankles and for some reason my one leg gets its more my Achilles tendon but if the tendons are all tight it will restrict the movement in your ankle kind "pull" the ankle and put stress on it. So if you think you legs are really tight or Achilles tendons just need to do some stretching and the range of motion will improve in your ankle.