I agree that a weight harness might be the best thing (I want one, but don't have the fun coupons available at this time), especially if you dive a drysuit, or think you will one day.
I have a weight integrated BC that I love, but if you go that route consider splitting the weight between BC and belt. Carefully evaluate how much weight you carry, now much exposure protection you use, and what will happen if you have to doff the BC at depth.
If you want a budget minded solution, consider this:
My weight belt has a big honkin' o-ring in the back to keep it tight. You could do the same with any standard (old fashioned) nylon weight belt.
To put the o-ring on the belt, pass the belt through one side of the weight keeper, put the o-ring around the belt, then pass the belt through the other side of the keeper. The o-ring is then held in place by the weight keeper, but goes around the weight belt itself. Make sense?
Then do the same thing again with the second weight keeper, capturing the other side of the o-ring.
When you are done the o-ring pulls a small loop of slack in the middle of the weight belt (sticking out away from your body). When you put the weight belt on and tighten it, the o-ring stretches and the slack disapears. Then when the weight belt stretches (as nylon does when wet) or your neoprene compresses (as it does when you descend), the o-ring takes up the slack.
The loop of slack in the weight belt only sticks out about 1/2" at worst, and is directly below your tank, so doesn't create an entanglement hazard. If the o-ring should break (mine has been going strong for over 10 years) all you would have to do is tighten the weight belt; it's still in one peice around your waiste, just with a little slack. Besides, the o-ring is really easy to inspect and replace if cracks start to develop.
Thrilled to be diving!!!
