Weakest Caps?

There's quite a few ships that could fit this. If you're interested in going by AoG, I'd say that the Brakiri Avioki is around as powerful as a Hyperion, ie, not very weak. The basic G'Quan pretty much sucks, though. It's variants make up for it. The Narn T'Loth also is down there. Most of the Narn ships aren't all that powerful, as a matter of fact. The Abbai Lakara is among the weakest capital ship in Ships of the Fleet Volume 1, also.

There's other races that could give the above a run for their money in sheer wimpiness, but they're in Militaries of the League Volume 2. There's also Raiders, which usually have crap for ships.