In many of my games ship level wasn’t very critical since all it did was increase hit points, and not that much either.
However, in my last game the AI seemed to be stuck technologically. There was no incentive for me to upgrade my weapons, so I had medium hull ships running around as my primary ships with 12/0/0 attack and 0/6/0 defense the whole game (7+ years). Many of the battles were somewhat even, and by the end I had quite a few med hulls that were Level 50 to 71 and with HPs that ranged from 70 to 112! I’d never seen this before, and it was extraordinary since Level 0 cruisers generally had ~24 HPs. One ship had as many HPs as a whole fleet (logistics 25)! The only thing I can think of is that, as mentioned above, your ships get more XPs when the attacks are more even (e.g. – harder), which was true in this case. Also, I only lost 1 med hull the whole game so the more experienced ships survived. Normally I try to build uber ships so that combat is a cakewalk, but in this case I was trying to draw out the game to get a diplomatic victory with tech trading off (note that I never was able to get the diplo victory – the AI simply refused to research Alliance and I gave up).
Hydro
In my most recent game I'm playing, I had similiar problem, with them just not researching that well. What I did was just give them Alliance, so that I could ally with them. I only gave it to civilizations that were close to me so that I wouldn't ally my enemies....
so turn on tech trading so you can give them alliance if you want the diplo win....