I think an important point is being missed in so far as single leg vs double leg jumping is concerned.
It's commonly stated that squat/bw ratios are less important for single leg jumping and that low bodyweight is of more importance for single leg jumping.
Realize this comparison is usually made between STANDING double leg jumping and RUNNING single leg jumping.
If we compared standing single leg jumping vs standing double leg jumping the difference would go away.
In laymans terms we can remember that any running jump involves (a) absorbing/translating force (speed) and (b) making force/speed quickly. A standing jump starts with speed==0 and thus only has part (b).
Obviously, the approach needs to produce speed and thus also requires strength. Indeed strength/bw will help more in for a 2-step approach single leg jump than a 4-step and 6-step and so forth. However, if you don't constrain the run-in length on a single leg jump you remove one of the benefits of strength/bw from the single leg approach jump. We recently submitted a paper on the optimal atmospheric long jump model.... essentially it's a sprint model with the parameter for drive phase removed. Because this parameter is removed it's not surprising that more athletes who have a more sleight build tend to perform well in the approach single leg jump. Don't make the mistake of assuming it's necessary to forgo strength and focus on losing body-weight to achieve a high single leg approach jump.... Sleight builds succeed, but success does not necessarily make a sleight build. Additionally, you can find great counterexamples in the decathlon, athletes of all build who achieve near elite marks in all types of jumps.
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As far as weight loss, I advise most athletes against long-term significant weight manipulation. Obviously, being obese is a bad idea. But if you are training hard and have any type of energy system work in your training (volleyball games, basketball games, sprinting tempo work, etc) you should achieve a manageable weight without intentionally restricting food, with the one caveat that you shouldn't eat complete junk sweets or drink alcohol. Athletes with no energy system work (Olympic lifters, jumpers who don't also run the 4x100) might have to eat slightly under their appetite to achieve optimal weight, but that depends on the individual.
Short term weight manipulation definitely has advantages for all athletes (a semi-fast the night before high-jump competition and a little dehydration the day of the event can pay dividends in a competition; especially when foolish competitors do silly things like carb-load the day before), but trying to lose substantial amounts of bodyweight can have unintended consequences that usually outweigh the benefits. Essentially, if you are fat, train hard, or don't eat completely horrible, then theirs a 95% chance you will lose weight. When you stop losing weight from that prescription then it's time to get stronger.