This is a very important thing to consider. Most of the slow motion videos I've watched have frozen the frame right where the skater's toepick is at before it leaves the ice. But is that skater still using their weight to lift themselves up at that time? I'd say it's doubtful.
It's not doubtful, that is what's happening (aside from the tiny little last bit of the toepick leaving the ice). The skater is spinning their weight around on the takeoff and thus making it so that they have to rotate less in order to complete the jump. This is part of why Triple-Triple combinations from women, especially more difficult ones, were more rare in the past. In order to do it "correctly", you need good speed out of the first jump and to go back into the toepick and up into the air. Now people just focus more on pulling into the landing of the first jump, dragging the toepick around, and clenching in for tight rotations. It's not actually about jumping anymore. It's about spinning a few inches off the ice.