Weak?
Ok then.
If you give the MK I's their max stats, at the cost of 2250 research (if you half the cost, since the research unlocks other things, it is a raw cost of 4500) it has:
The corvette does have one thing, it is cheaper at 60% the energy and around 70% the cost. That's the end of the good news.
With the shields, the corvette has less then 60% of the HP as the frigate with max shields (8 million base + 6 million shields versus 24 million base)
In terms of max dps, the spire frigate shoots its one beam every 3 seconds (1 second reload, 2 second fire) for 1.8 million damage.
The spire corvette shoots its beam every ten seconds (8 second reload, 2 second fire) for 1.2 million damage. The MK II lasers max damage can do an additional 108k damage per second against its best target.
Let me say this in another way: The spire frigate, a basic core ship, does over 2 times as much damage as the spire corvette in max damage. Even if you exclude the increasing disparity in research cost, the spire frigate is equal if not better then the corvette in general usage.
It would be fine is the spire corvette was core, but it is not. Just as it would not be OK to say the bulletproof fighter would be OK compared to the basic fighter if it had less then half the max dps and at most 60% of its HP because it was bullet proof, the spire corvette is not OK to have less then half the max dps as its core cousin because it is more flexible while being unbelievably frail compared to the otherwise frailest starship.
Only if you divide both spire craft's lasers by a third, while maintaining the laser's max dps, do the two even obtain parity in damage right now.
tl;dr
Spire corvette costs 70% as much, at best with 58% the HP, around the same dps (spire frigate comes out in max dps), and the frigate is always avialable with a modest K cost while the corvette takes a bonus ship slot and a significant K investment.