Weighted how? That is better! But it still worries me... a weighted barrel can still roll if there isn't something physically stopping it... but I may be a bit of a worry wort when it comes to the safety of fences.
Anyway, I know how you feel. For the longest time I thought 'ugh ew' when I saw photos of myself, but now that I've been consciously working on my position I feel better. It just takes time! Basically, when you're coming around a corner or around a turn you want to be pushing with the inside leg to bring your horses entire body through the turn and keep the impulsion, without letting your horse drop to the inside, thus throwing them off on the approach to the fences and throwing off their balance. I used to have BIG problems riding entirely off my hand, I learnt quickly when my horse decided he'd had enough! Have you done any 'spiral in - spiral out' exercises? I don't know what other people call it so I'll describe it... ride on a large circle, preferably in the center of a ring where your horse can't balance himself off of the wall, and use the pressure of your outside leg to gradually push your horse in to a slightly smaller circle, and continue until you're in a 5 or 10 meter circle (sitting the trot here usually helps) and then do the same process to push your horse out gradually to the bigger circle. The goal is to use your inside leg to keep your horse bent and have your horse moving OFF of your leg, with support from your outside leg to keep your horse from bombing back to the rail with minimal use of the reins.
Lots of leg yields are also helpful before you start doing any serious short turns off your leg pressure. Essentially, if your legs aren't strong enough to achieve a proper bend (which, chances are they aren't if you've been relying on your reins for too much) it will be difficult and frustrating. You need to build up YOUR muscle AND your horses muscle.