Was just shown this thread as I did post a rather similar question.
I don't want to be a spoilsport, but as a Practitioner of Kung Fu and Kickboxing, I just cannot leave the last phrase uncommented:
Kicking in the door at the Head Museum in SP3k was no small feat either. No matter how good she is at Arcturan Kung-fu, that takes raw power.
I am very sorry, but you are wrong about that.
You see, a punch's/kick's impact is in fact NOT mostly based on raw power, your muscles, etc... . When you punch, you leave your arm as relaxed as possible, and strike as fast as you can. The very last moment before impact, you built up tension in your muscles.*
(Same with kicks). It's rather your ability to pass on an impulse properly to your target, than your physical strength. (In my old Kung Fu class, I was rather average strength wise. Yet I was the one who could by far deliver that hardest punch (expect our coach, of course...
Okay...I have to admit this is nitpicking to the max on my part, but when you train something trice a week for years, it's probably normal to get picky about the proper details;)
About the gravity having no effect on her:
She was probably just clever. When you stand in a hunched stance, your knees bend, etc... , you need to apply muscle strength to keep that way. Standing straight is in fact much easier. Imagine yourself pushing a car: Would you do so with stretched or bent arms? Stretched, of course. There is a reason your joints can be locked;) Or try to stand a while with your knees bent in a deep stance, and try the same with your legs straight.
Examine that scene closer: Brannigan and Fry have a rather slouched stance, knees bend. The gravity pushed them forward, and their knees have a direction in which they can give in. They had to fight the gravity to get upright, and also apply strength to their legs.
Leela stood more upright, so no weight cloud push her forward. When entering that planet, her knees gave in, but she immediatelly streched them. (she had to do one just movement, straightening her knees, and could put all her strength behind it...while Brannigan and Fry had to use their strength to keep their balance, tensen their back muscles, and tried to keep their knees from giving in, though they were already bent way too much to be able to get up again.)
*Okay, when practising martial arts, your strength will sooner or later get above average. But not to a degree as a e.g. say weight-lifter.