Weyland's desire to meet the aliens, to ask for more life, THAT makes sense....
Actually, even that doesn't make much sense. Prior to the launch of the mission the movie presents no information to even remotely suggest that the beings depicted in the cave paintings are our creators.
Aliens from another world, yes, definitely, but not the slightest scrap or clue that these beings made us and have the ability to prolong human life.
Someone, presumably Shaw, jumps to the conclusion that these aliens created us. She somehow manages to convince others of this, including Weyland. How I don't know, as she has no evidence. I guess she just chose to believe, and Weyland inexplicably chose to believe her.
So perhaps it all makes sense. Weyland was a senile old fool who gathered together a group of clueless idiots on a fool's errand of epic proportions.