Did Vegeta want to make Gohan stronger?
This question is a little open ended, I could not find any material supporting a definite answer. One could surmise that since Gohan is one of the last Saiyans he doesn't want to completely wipe out the race. It is already understood at this point in time Vegeta did harbor a lot of anger towards Goku and if that would have been Goku in a weakened state he probably would have killed him. Vegeta maybe saw no challenge in killing a child Saiyan or maybe he thought Gohan could come to be a potential challenger one day and would rather wait for that fight then kill him right there.There are a lot of answers that could be generated for this question. Until hard supporting material can be found it can really be anyone's opinion as to why he didn't kill him.