Well the formula was in all likelyhood not made to calculate the power of a body. It's like that infamous thing about bumblebees not being supposed to be able to fly. Except it does, so there's obviously some variables the model didn't include. (I think it was that they turned their wings in different angles while flapping, to create some extra lift) There's probably a few extra variables in there just from how a body moves. I'm no matematician or phycisist though, just stumbled upon it.
Weight, would mean, mass in this context. Imagine a device that throws rocks in a lab or something.
A 50 gram rock thrown at a certain speed gives 1 unit of kinetic energy.
A 100 g rock at the same speed would give 2 units of KE
But a 50 g rock at twice the speed would give 4 uits of KE.
For a body, apart from fistloads and so on I guess it would have to mean muscle power and bodyweight set in motion. And I'm pretty sure the speed of mobilizing the whole body quickly runs into limits on i.e., how fast you can fall (drop step), overcoming inertia and so on. Not that my knowledge in this domain is by any means extensive.
The way I saw it explained one place mentioned it in the context of weapons. Ie., a stick. It should weigh no more than what you can swing easily around at maximum speed. That should give the most effect for the effort. Seeking a similar sweet spot should work unarmed. But there are a lot of other factors that come into play when exiting the lab and messing with ambulatory meatbags.
Accelerate vs constant speed? Don't know. But I suppose that if you're within a range from which you can be explosive, you won't be slowing down before you make contact as it will be well within reach. I've only been skimming through it so far but a book called Martial mechanics, by Phillip Starr goes over a lot of stuff on how to squeeze as much as possible out of your strikes. It seems well worth a read. It's the second place I've seen that mass vs speed thing too btw.