As alluded to in the comments, you should look at your core strength and go see a good physiotherapist or personal trainer to get an assessment and see if they can recommend some strengthening exercises.
Also, it sounds like you're suffering from pretty severed anterior pelvic tilt (that's a guess based on reading a sentence you posted on the internet, don't read too much into it, it's not a diagnosis, you need to go see someone in person for that). If you are, then that would explain the sticking out belly, why it feels like you're constantly leaning back and have a curved thoracic spine so you can see in front of you. Do you also get knee / hip / back / shoulder issues? If so, that's another possible sign.
You say you're good at sit-ups, but depending on how you're doing them, you could be relying heavily on your hip flexors to pull yourself up, causing them to tighten and shorten, which would only exacerbate the problem.
I started out my answer by writing this, but realised it was more of a story than an answer, but I'm leaving it in because I always think personal stories are often more impactful than a series of facts.
A long time ago a friend of mine had something short circuit in her brain which resulted in a rather more rapid than planned descent of a staircase. She spent a little while in hospital and then in a wheelchair, and once she came out of the wheelchair was deemed to be more or less fixed and told to carry on with the hospital physio just to make sure everything was ok.
The problem was, the way she walked akin to swinging one leg forward, throwing her weight over that leg, doing the same with the other leg, and hopefully making it where she was aiming to go without stumbling into anything.
Her legs were strong, rehab had seen to that, but she still couldn't walk properly. The sessions with her hospital physio consisted of some leg strengthening on a pressing machine device, and walking on a treadmill for time. This went on for months before she finally got fed up and found a different physiotherapist to try and help her.
The second physio did a few tests and pointed out that she had "forgotten" how to engage her core when she walked, meaning there was no balance there and very little control, which is why she had to throw herself, do or die style, into walking across the room.
Once she started working on her core strength, everything improved dramatically; walking became easier, she no longer stumbled around. She could take the dog for a walk without worrying it was going to pull her over, go out in snowy weather and not worry about slipping and falling. Fast forward several years and not only can she move normally, she's also a pole fitness instructor, teaching other people how to get stronger and improve the way they move.