Does obesity make you shorter?

I mean so if an obese adult loses a significant amount of weight, does it impact their height one way or another?

Not unless you had a lot of fat on the bottom of your feet.

My height remained the same from obesity to non-obesity. One thing that could have an impact is posture. People carrying large amounts of weight tend to sag and hunch over, so someone who lost a lot of weight might stand up straighter and appear to be taller.

I agree with this. I’m 40lbs lighter than I was a few years ago, and my posture has improved quite a bit.