I had to stop his excess of resources before I was overwhelmed, so I attacked his nearest ice planet with a newly built KOL and my leftover Cobalts and Siege Frigates. He spammed a lot of frigates to try and defend the planet, eventually wiping out all my frigates....at the expense of a lot of his frigates and an extra level for my KOL.
It sounds like he would just send frigates one by one to try and beat off his forces? If so, that was a mistake. As Ron has mentioned, 10-ish Cobalts can destroy a low level capital. If your Kol had its damage reduction ability it would have been harder, but if he had waited to collect all his frigates and send them in at once, chances are you would've had to tuck tail and run.
There is something wrong when ALL those frigates can't take down a single cap ship (with minor upgrades).
In our last big game, I had a fleet with a single level 2 or 3 Sova, along with about 8-9 Cobalts and 10-11 I think LRMs. I don't remember the exact numbers. With that force, I engaged a fleet of a level 3 Marza, level 2 or 3 Dunov, and a level 6 Akkan along with a handful (very few, though) cobalts. The Marza was destroyed, the Akkan managed to jump at about 10% hull, the Dunov also retreated and all of the cobalts were destroyed. My losses were a few cobalts and a few LRMs, my Sova had probably 75% hull hp remaining. I gotta tell you, most of the damage came from the frigates, not my Sova