I have actually seen all of these films except the first and considering Roger Ebert named it one of the greatest movies ever made, I think its safe to say he's one of the best.
As for the Oscars well he has the misfortune of making his classics in years when there are bigger noises. 1985 he's nominated for Witness but everybody is upset about the fact that Steven Spielberg WASN'T nominated for directing The Color Purple. That year Akira Kurosawa and John huston were nominated but for some reason the Oscar went to Sydney Pollack for Out of Africa.
Dead Poets Society, everybody is outraged Spike Lee wasn't nominated for Best Director OR bEST Picture for Do The Right Thing (rightly, I might add) Oliver Stone won for Born on the Fourth of July and honestly I would rather Dead Poets Society have won Best Picture instead of Driving Miss Daisy. (The movie did win Best Screenplay, did Weir write that? I forget)
Weir was nominated for The Truman Show but the film wasn't nominated for Best Picture. They nominated Life is Beautiful instead which still enrages me twenty five years. Weir was up aaginst Steven Spielberg for Saving Private Ryan and Terence Malick for The Thin Red Line. No chance.
He was nominated for Directing Master and Commander but even if Peter Jackson hadn't been there, his competition was Clint Eastwood for Mystic River and Sofia Coppola for Lost in Translation. I've seen all four films, realistically speaking Weir was the fourth best choice that year.
He was also nominating for writing the romantic comedy Green Card in 1991. He lost to Bruce Joel Rubin for Ghost. I'm not sure who the other nominees that year were.
Weir is just one of those directors like Ridley Scott who everyone knows is a master craftsman but whose never won a Best Director because of timing more than anything. It's not quite as ridiculous as Robert Altman or Sidney Lumet never winning for Best Director (those two are my candidates for the most glaring discrepancies by the Oscars over the years) but is a shame.