isn't as bad as it looks on paper. It's major advantage is that it is hellaciously tough and difficult to kill. Now I know we all have visions of how easily the Shadows spanked the Narns, but remember... Those ARE the Shadows we're talking about. A good example of how tough a G'Quan is would be the stand-up fight it had with the Primus near B5. Ultimately both ships went boom, but if memory serves, the Primus folded first. Okay, I know, the G'Quan had help from the station's 'furys, but the fact remains, the Primus folded first. And many of the times we see a G'Quan going down, it's after either an ambush (the Centauri attack in 'In the Beginning') or sustained pounding.
Anyway, to answer your question...
The WEAKEST capital ships were never seen in the show. I'm assuming you mean "military ships" since there's a lot of freighters large enough to be capital ships, but they aren't military vessels. The weakest military ships are, generally, military freighters and Gaim ships. The Gaim have no ship-building facilities of their own until after the end of Season 5 and as a result they've been forced to buy the cast-off hulls of other races and refit them for service. This means they're generally using whatever's so obsolete in another race's navy as to be worth selling to a potentially hostile alien power.
About the only things that make Gaim ships competitive is the way they refit the hulls and the weapons they mount. They refit the hulls with immense, solid bulkheads that make the ship very hard to blow apart. You pretty much have to blast sections off one at a time, and this isn't always much of an option when being pounded by return fire. Their weapons are oddly advanced for such a young race. In fact, they've stumbled on a kind of weapon that has similarities in the way it functions to a Triad weapon. The Triad are the second oldest of the First Ones just behind Lorien's people! Talk about dumb luck, huh?
Other weak capital ships belong predominantly to the weakest of the weaker races. Grome, Hurr, and Alacans all come to mind. Those races are detailed in Militaries of the League 2, which I don't have at the moment. When I get 'em, I'll try to give you a better rundown on their capabilities. Actually, now that I think about it, the Alacans are detailed in the Dilgar War material. Their species was nearly wiped out in its entirety by the Dilgar. There's a couple other races that were similarly driven to the brink of extinction.
Abbai ships are considered weak by some, but mainly due to their weak offensive punch. The Abbai are hardcore pacifists who hate war and hate needing weapons even more. As a result, their ships are heavy on defenses and light on offensive weaponry. Don't be lulled, though. Their defenses make them hellaciously difficult to take down if you don't know what you're doing. We're talking good armor, gravitic shielding, communication disruptors (to kill fleet cohesion), some of the best anti-fighter weapons in the League, particle impeders that are dedicated "interceptor" weapons, and more... When the Dilgar Wars swept through their space, they pulled back behind their orbital defenses and let the Dilgar pound themselves to bits on the OSATs and Starbase in orbit around their homeworld. Eventually the Dilgar said "screw it", posted a blockade fleet, and went on to more pressing matters.
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