Levein is under plenty of pressure following his side's very poor beginning to their 2014 World Cup qualifying campaign - which already looks over - but Weir is of the belief that he is the right man for the Tartan Army job.
"We should expect better results but there is such a fine line between winning and losing," said Weir.
"There is no better example than the Wales game (last Friday). We were winning 1-0, relatively comfortable, scored another great goal and the game was probably finished.
"The goal gets disallowed and Wales go up the other end and score and we end up losing the game. To qualify you need everything to conspire for you.
"It is difficult but the players obviously do believe in the manager and believe what he's preaching to him and his structure, and that goes a long way. Things have conspired against us, we have probably not had the rub of the green.
"Ultimately everyone knows you are judged on results. But I don't think you can question the detail the manager has gone into and the atmosphere he has created, and he has got the best players there.
"It's very difficult to qualify but he seems to have got the players behind him and is doing the best job he can."