Tom wasn't weak. His training was as a lawyer, and lawyers are trained to be conciliators, to work out practical solutions before going to trial (or in the Corleones' case, shooting). Vito chose him for his brains, his loyalty to the family, and because his even temperament was essential in containing Sonny's hot-headedness and his penchant for violence. He wasn't a good match for Michael, who didn't have Sonny's problem and was his own consigliere. Michael was cruel to him at times, but as we saw, when the chips were down (i.e., after Vito's death in GF and after the Tahoe shooting in II), he trusted Tom.

If Tom had a weakness it was that he wasn't Sicilian and didn't think like a Sicilian. IMO, he should have seen that Carlo would look for vengeance (in the novel, he realizes that he was "no fit wartime consigliere--old Genco would have smelled a rat"). Michael may have (unfairly) blamed him for Sonny's death.