This is tough because often times the "weak" characters portray the most strength in character.
Physically, Lennie is clearly the work horse in the story, but mentally he is much weaker than his counterparts. He is "slow". He is very childlike in the story and often times has to be treated as such. He also does not have a very strong grasp on his emotions. He cannot channel his feelings in a normal way and often times in the story his feelings of anger are expressed with a violence that is more intense than his actual feelings. For example when he killed the puppy or when he killed Curly's wife. Each instance was a true accident because he didn't mean to kill them, but his expression of anger got away from him. This display of his weakness should not downplay his strength of character and his undying loyalty.
Curly's wife could also be another character that is perceived as weak. She is pretty and knows it, but she is also a victim of a loveless marriage to a very insecure man. She is weak in that she lacks affection and seeks it in the wrong places. This weakness was ultimately her demise in the story because she flirts with Lennie, knowing that he was "slow", and Lennie did not know how to handle the sexual feelings she aroused in him. If she had been loved she might have lived, but her need for affection was her ultimate weakness.
Sure…but weak in what sense?
If you mean weak in the sense of not having strong wills/a focused sense of self, I'd say that the weakest characters are Candy, and, curiously, Curley. He's so threatened by his wife that he has to lord it over the other men via his position and threats of violence.
If you mean weak as in badly drawn or characterized, I'd say that Curley's wife is a bit of a stereotype, and that Slim is too pure.