The concept of mitigation so far was that it was the amount of damage a shield could stop per hit, with the excess going through to the ship's armor. Every point of damage the mitigation of a ship stops reduces the shield total. Any it doesn't stop reduces the ship's structural points.
However, anything that's rating 4 or less on the mecha weapon scale would *plink* or *bzzt* harmlessly on a starship-grade target.
As for weapon limitations, this goes more in the realm of ship building, but I'd consider any ship bearing enough weapons to do half its SP in same-grade damage to be well armed. The closer your weapon loadout damage potential gets to the ship's SP total, the more it can be considered an attack ship bristling with weapons for its size.
Current designs exceeding their own Structural Point totals, can be balanced from the get go in a couple of ways. Some involve accepting to tone down certain weapons to the mecha-scale so to maintain point-defense firepower without having these weapons be significant on the ship-scale. Another is to consider having some of those weapons have a much slower charging time to limited cycling use, or to have them be single-shot in a fight or limited to a few shots (if the ammo restriction is significant).
It wasn't my goal to make policy on how to build ships with this, as I felt it ought to remain fairly freeform as long as common sense applied. I'd note the above suggestions inconvenience me too: most of the Mishhuvurthyar ships are bristling with weapons. I'd need to give them a huge overhaul or simply scrap them (including the flagship type, which is quite guilty of the exploiting abuse Jess pointed out).
Also, just as food for thought: I'd imagine that a weapon with a high damage output is much more likely to deal more compromising damage on a target than a weaker one. You can go and fire 1 damage anti-ship weapon on a cruiser target and it will be able to take it - however, a GM could easily interpret that such blows would be surface hits, not penetrating deeply to damage the more delicate internal workings of the ship - effectively, the armor is doing its job of protecting the insides of the ship. Still, pile these hits up and it's quite possible to deal the opposing vessel death through hundreds of papercuts.
A more powerful weapon, though, is much more likely to punch through deeper and damage the internal systems, decreasing the ship's performance, damaging weapons/power systems/engines/shield emitters and such. The current scale has a level of lethality suggesting that a ship can take 10 hits of a same-class weapon before being crippled/destroyed... but if you end up using a stronger weapon than that, of course it's going to smart more. Shields so far double a ship's staying power, though more reliably so as long as the said ship fights something its size-class or smaller.