No, you don't want to stay leaned back either.
There is an old saying that if you look at the ground, that's where you'll end up. The thinking behind that is that if you get to looking off to the side, that throws you off balance and you get dumped.
Here, on a bull, you can see how the rider keeps his gaze settled right in the middle of the animal's motion, almost like he's just watching the bull's shoulders. An animal can't go anywhere without his shoulders so if you keep them firmly in your line of sight, you have a better chance of sticking with him. Horses and bulls can sling their heads all over the place; up, down, toward their motion, away from their motion, etc, but their shoulders can never go somewhere that their body does not.
The actual ride is about a minute in.
And here's the same guy on a saddle bronc. Actual ride about 4 minutes in.
As for your size, they often use the same horses for both saddle bronc and bareback, and, since people are generally getting bigger, they prefer bigger horses. Many of the bucking horses we see these days have at least some draft breeding in them to give them bigger bones and feet and a bit more mass for the bigger cowboys.