「待って」と「待っていて」の違いは何です？
I've been reading about how the 「ている」 form isn't actually an "-ing" but rather more of a resultant meaning and that's fine, but I don't really get how this relates to requests in the -tete sense. Hell, the "-ing" never really made sense for requests in the first place.I just had a thought, could it be requesting to change to a state/result of said verb, i.e. (Please) change to a state of waiting?

Question

「待って」と「待っていて」の違いは何です？
I've been reading about how the 「ている」 form isn't actually an "-ing" but rather more of a resultant meaning and that's fine, but I don't really get how this relates to requests in the -tete sense. Hell, the "-ing" never really made sense for requests in the first place.I just had a thought, could it be requesting to change to a state/result of said verb, i.e. (Please) change to a state of waiting?

Answer

待ってください 。= Wait a moment please.
待っていてください。 = Please (stay here and) keep waiting.

Maybe it's easier to catch the difference between both forms using another verb:
見てください。 = Please look at this.
見ていてください。 = Please keep your eyes on it.
赤ちゃんを見ていてください。= Please keep an eye on the baby. (You're asked to keep performing the action for a while)