1. He was a "Mary Sue" character. This term refers to a character who has a solution for everything such that he or she makes the other characters in a story irrelevant.
2. Isn't that kind of...not true?
3. He was hated because he was the usual Hollywood concept of a bright child. And Hollywood always makes bright children insufferable, perhaps because they feel that will win acceptance with average children. These characters tend to be hated by bright children who don't feel that being bright means you automatically must be clueless in other ways. (See the current show Bones for an older example of the "Bright yet clueless" sterotype).
4. I don't hate him. However he wasn't really like a true officer. And so you can't really respect him as much. And for whatever reason. Picard telling Weasley to shut up keeps sounding on.
5. When NG started, it threw die hard Trek fans into a tizzy. The new ship was less rigid, with a more organic design. The uniforms were updated and had a weird jumper style (like for toddlers) look, along with those darn shoulder pads. All the old character types were represented more or less, and it also kept with the concept of interracial crews. So the only new element that could be included was--a young boy learning the ways of flying a star ship. It made perfect sense in the nautical way. Often a ship sailing off would have a young man aboard at the behest of an elder sailor or patron. The "child element" just didn't sit so well with old Trek heads, as they felt it lessoned the militaristic aspect of the ship. One would not see a young boy running around the control bridge of a Nimitz class aircraft carrier, right?
Wasn't he in that movie about the private boarding school that gets taken over by South American terrorists
What about the episode where Wesley comes back, gets laid, and saves the ship?
That rainbow sweater he used to wear may have been a factor.
It's a shame that so many Star Trek fans couldn't separate their hatred of the character from their hatred of the actor. Wil turned into a pretty cool guy.