In Winter Soldier he was basically a retired soldier who WAS a "formerly athletic, pudgy face nigga in his late 30s". He was getting lapped up by Cap trying to get some exercise in. Joined up with Cap because he believed in him. He brought out the Falcon wings and was rusty as heck, but still did a good job considering all that.

But by the time we see him in Civil War he's been running with Cap for a couple years side by side doing missions all across the world. So yeah, he's in way better shape, and yeah he has a ton more moves while flying and fighting.