The lighter you are, the less weight your muscles have to propel in a jump -- so yes, losing body fat will make jumping easier. But that's not the only way you can, or should, increase your jumping power. Strengthening the engine that powers those jumps -- that is, fast-twitch muscle fibers that excel at powerful, explosive movements -- and the mastery and confidence that come with frequent practice will all do wonders for your jump as well.
Practice What You Preach
As a general rule if you want to get better at something physical, you have to do it -- repeatedly. So to improve your jumping power, you'd need to do exercises that require -- and build -- the same explosive combination of strength and speed. That doesn't mean that you have to do the exact same kind of jump you're training for constantly; instead, mix it up with plyometrics that mimic or complement your goal jump's biomechanics. Think ski jumps, box jumps, bench jumps, skate jumps, bike jumps -- sometimes called lunging jumps -- and so on.
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Jumping exercises place sudden, heavy loads on your muscles and connective tissues. Limited range of motion, age, excessive body weight and inadequate muscular strength and endurance are all potential contraindications for jumping exercises, just because your body isn't quite up to managing those sudden loads without injury -- yet. If you're not sure whether you can do jumping workouts safely, ask an exercise or medical professional for help.