OP, I don't think you should leave decisions about proper weighting entirely to your instructor.
Here is one approach you might use to get an initial idea about the weight you should be wearing. (This approach was taught to me by my OW instructor in '86; he had taught this approach since the mid 1960's, and he still teaches this approach today.) Of course, it depends on your using a "reasonable" cylinder (e.g., steel 72), a "reasonable" BC (one that is approx neutrally buoyant when completely empty) and a full 2-piece 1/4-in wet suit (with boots, hood, and gloves/mitts) made of a better quality neoprene (i.e., small bubbles).
Dress in your complete gear, with your tank completely full, but with your BC completely empty and no air trapped anywhere in your full wet suit. Wear a weight belt. Breathing through your snorkel, take a deep breath, and hold it. Relax. Don't fin. Be heads up, fins down in water only deep enough to permit this. OK. You should be floating at eye level. When you exhale, you should slowly sink beneath the surface. Someone should be assisting you when you're figuring out your proper weight; that person can hand you weights or take weights from you as required. When you've got your weight figured out, put all (or nearly all) of your lead on a weight belt. That's all there is to it.
One of the open water skills we were required to do was called the Three Mile Swim. Weighted as above (with a completely full tank and a completely empty BC), we would have to surface kick, in the prone position, a distance of three miles while breathing through our snorkels and towing a substantial dive float with flag--through wind-driven waves, boat wakes, currents, etc. Actually, we had to surface kick 1 1/2 miles one-way, complete some surface skills (e.g., weight belt removal/replacement), and then surface kick the 1 1/2 miles back while doing other skills (e.g., buddy tow). One of the things this skill is meant to reinforce is that with proper equipment and weighting, you really shouldn't have to be overly concerned about a BC failure, for you can always swim yourself up from recreational training limit depths to the surface even with a failed BC (since your "reasonable" tank and BC can never be too negatively buoyant), and, once on the surface, you can always surface kick back from a considerable distance--all this without having ditched anything! (And you can always use your surface float, if you need to, to stop and rest.)
I hope this helps.
CAVEAT: I am NOT a scuba instructor.