Except "that solution" is actually a set of usually thousands, if not millions of solutions some of which are really good fits and some of which are terrible. There ISN'T a single solution with a GA; there is a solution space (a set of solutions) that have varying degrees of fitness based upon how you weight.
Typically at the end of a GA run (at least my runs, with populations typically maintained at 50,000) you end up with a population where the top 1,000 are all EXTREMELY good and solid answers! The next 10,000 are also really good, but not as good.
Then I go and choose one of the top 1,000, and often that choice is based upon other external variables (like with the filter, I may limit my solution choice to what components I have laying around right now, so as to minimize the number that I have to order).
GAs don't just "give you an answer"; they give you a large set of potential answers, and the fitness of those answers - and the size of the set - both grow over time.
And nowhere in the process of generating those "solutions" is there any hint of the weighing? I really doubt it.