There are several styles of riding. I don't know which you prefer.
Most western riders do it Kayty's way, which I believe is also taught in dressage: weight in the seat, legs draping the horse, and your hips moving in synch with the horse. My favorite video example is this:
That isn't exactly dressage, but it shows how a western rider with weight in the seat moves with the horse so that his weight won't interfere with the horse.
Another approach is a forward seat. It uses more weight on the thighs and less in the rump. The rider's center of gravity is typically over the stirrup bars, and the rider's upper body is tilted somewhat forward. At an extreme, it looks like Gen Patton:
But more often like this picture (blurred, taken from a book by George Morris):
Sometimes how you ride is driven by the saddle. I dislike my Circle Y saddle (although my youngest daughter refuses to ride in anything else), because the shape of the saddle forces my thighs to be almost parallel to the horse's back. I feel like it puts my weight all above the horse's back, and I feel very insecure in it. It does the same to my daughter, but she loves it and rides well in it. Although we were stopped in this picture, you can see a big difference in how we sit in a saddle - but if I use the Circle Y, I am forced to sit like my daughter does:
So, what is right?
If you don't compete, then it is up to you and your horse. I feel most comfortable with a *******ized version of a forward seat. That may be due in part to a back injury 4 years ago. My daughter NEVER uses anything like a forward seat. Our horses don't seem to care.
There ARE faults with any style: gripping with the knee is bad, and bracing between the stirrups and cantle is almost always bad too. My lower back doesn't flex well, so I tend to prefer more weight on my thighs and less motion with my back.
And BTW - I'm not an instructor, trainer, pro rider, competitor or anything else in the horse world. Just reporting on what I've seen & tried over the last 4 1/2 years, and how it has worked out differently for my daughter and I.
If you have any pictures, it would help folks to see what YOU are doing, and give tips on how it might be affecting you & your horse.