Ah, how interesting! I've been told by a bunch of people that I walk funny, I believe I have a weird walk as well and sometimes I actually feel insecure about it, I feel like I'm standing out.
I'm pretty tall for a girl and over the years I spent a lot of time hunched over, especially throughout depression & anxiety time when I would just want to disappear, so I struggle to keep my back straight and have to remind myself all the time. As for the walk itself, it's like the legs go first and I go second, it's a bouncy, floaty walk. Usually when I have to take a walk through the city, with people around, and I haven't done it in a while, I will literally feel like I don't know how to walk and it will be hard to find my center of gravity. It's like I could start flying anytime now.
It does help to exercise. The more physically active I'll be, the more grounded I'll feel. But still, I feel a bit goofy but lately I've been trying to embrace all my eccentricities and accept that if I stand out, it's alright, it's just who I am.