Dude is supposed to be a child prodigy on the ship. He solves problems better and faster than everyone else who are way more qualified and experienced and intelligent at their Stations. He comes off as pretentious.
He also lacks even a modicum of wisdom, despite being surrounded by wise role models. He almost destroyed the Enterprise twice, and he wasn't even a real member of the crew. When he went to the academy he got some other kids killed because of his lack of wisdom. I get that he's a kid, and kids make dumb decisions, but Wes made some very large adult sized mistakes.
To be fair that is also because the 'wise role models' accepted him as part of the crew and let him make those mistakes. You can't fault the kid who jumps at that kind of opportunity and lets it get it to his head a bit. Going back to school when your cool wise role models let you fly a real starship must be tedious.
Supposedly a child prodigy, yet fails to get into Starfleet Academy. Then magically pulls the solution out of his Crusher.
I like him, but there could've been more done with him to make him a part of the crew and not a mary sue self insert. Sadly, the actor made a decision to leave and couldn't get the screentime for that.