I've rewatched seasons 1 and 2 recently and didn't find him as annoying as most. There is a fair number of episodes he's not even in or doesn't do a whole lot. And he wore lots of ugly sweaters in season 1. I think like anything else, the writers were trying to figure out what to do with him and it just went badly most of the time, but I like the closure they eventually gave him. And at least someone figured out that if they want to make "Wesley wants to go to the academy" thing believable, he would have to leave the show. Unlike Voyager where we had to believe Kim was never better than an ensign.
I really like Wil Weaton though. His recent appearances on The Big Bang Theory have been great.
I never did understand why Kim never got a promotion from Janeway.... even after seven years. He's probably my least favorite character on Voyager, just below Nelix, but he had some brains to him and should have eventually grown beyond Ensign.
But that's another topic I suppose.
W. Crusher.... well I never had a beef with him and never got what the big deal was over him (in regards to hating his guts)
As I saw it.... he was smarter then most his age, he took personal interest in star ships and starfleet, mostly because his parents were in starfleet. Picard didn't want any children on his ship, let alone on the bridge, but when he was told it was Beverly's son (the son of his best friend whom he felt responsible for him dying) he gradually moved into the father figure roll for Wesley..... though when he started to out show Picard and know the bridge so well, Picard obviously snapped back into his stuffy mode and ordered him back off the bridge.... but he saw his potential, and I think he had some personal interest in the kid.... so based on all that, he made the decision to let him on the bridge, to give him acting ensign rank and to nurture his abilities, especially after the traveler mentioned about his future. I imagine if it was any other captain, he wouldn't have had such special treatment given to him.
I see him no different then a kid who grew up around cars, who had a father as an auto mechanic and can work on engines at a young age..... some kids tend to focus or specialize in certain areas.... that's not their fault.
At a very young age, I could draw better then most adults, and in my teenage days, I was drawing better then most art college graduates...... just because someone is older and had training, doesn't mean they should automatically be better then someone younger who spent their own free time learning how to do the exact same things..... nor should they be shatted on for being better or par.
It wasn't my fault some of my work was better, nor did I boast.... but others liked my work and encouraged me to go farther.... if I was better and younger then someone who was trained in the same field.... well that's their own problem not mine.
As I see it, their own anger is more towards their jealousy of someone younger and smarter out-showing them... or insecurity of their own abilities. Nobody should be treated like crap for simply knowing what they know or having confidence in their own abilities over someone who's older and was doing the same thing for longer.
I'm not the best at what I do, nobody ever really is, since everybody has their own unique style..... but I'm also aware that there's a chance that someone younger then I will end up being better then I.... that's life.