I don't know how old you are, but at 58 I've been dealing with a similar issue. When I was younger I never had the problem of a "gut" that stuck out.
I'm also pretty tall--probably about a half inch taller than you. When I gained weight (about 20 pounds as well), I started having the same problem. It seemed like no matter what I did, I couldn't get rid of it. I never had the problem of weight going to my belly like that.
I do think some is bloating (it can relate to what I eat at times), but in the end, the only thing that worked was losing that 20 pounds again. While it's not perfect, my belly is pretty much gone, and now I don't look pregnant from the side!
I wish I could give you better news!
If you're super young, I don't know if this will relate to you, but as we're similar height, weight, and body type, I related immediately to the problem.
Take care, and good luck!