There are lots of old sayings or rules that were passed down through the generations concerning roping. One of those that I hear a lot is that you should stand up to rope. I see some students that were taught that, and they literally try to stand up out of the seat of their saddle to ride and rope. The majority of the time doing that leads to a balance problem with heeling, because of the turn you have to make (the corner) and the stop.
The balance problem in the majority of people I see who stand up to rope is a back and forth, teeter-tottering with their upper body. When the horse starts to stop, it tends to throw them forward, because it's hard to stabilize their upper body from a standing position. The reason I notice that is because when I was a little kid I started roping without the use of stirrups. My feet rested on top of the stirrups, with the calves of my legs between the stirrup leathers. So I was sat down and locked in. I sat right down on my butt for the first six years I roped. I was 12 years old before I ever rode a saddle that fit.
Because of the corner and because the majority of heel horses are looking for your throw and wanting to stop, to be able to sit straight up and down and ride your horse into position is an important part of getting a good throw every time. Plus, if your body is in a straight up-and-down position you can get a proper angle on your swing, which leads to the proper angle on your delivery.
From how I learned to ride as a kid, I learned to balance my upper body through the contact I had with the seat of my saddle. I like to be in the front of my saddle, with my legs and thighs against the swells, as opposed to the back of my saddle. Having some weight in the seat of my saddle and that contact through my legs is what I use to stabilize my upper body.
I use my thighs down to my knees (that's the part of the leg in contact with the saddle) to balance my upper body. That lets me use the lower parts of my legs to ride my horse and kick. Guys who stand up use their knees down for gripping their horse, standing and supporting their upper body, so it's hard for them to kick. They tend to lean forward to ask their horse to keep moving, but when you do that and your horse gets short it tends to throw you down in your upper body when you throw. (David Key is heading here.)
Stirrup length is important, and the size of your seat affects that length. The longer the seat of the saddle, the shorter your stirrups should be. Your stirrups should be adjusted to bend your leg and bring it up to the swell of your saddle. If you have a saddle that fits you better and tighter you can get away with a longer stirrup length, because you're already up close to your swells.
I ride a 14.5-inch seat. When I stand up, I like to just barely clear the seat by about an inch or so. I ride with my knees bent and probably 40-50 percent of my weight in the seat of my saddle, but still keeping contact with the seat and swells of the saddle for my balance support and stability.