As best as I know, you will fly either TAME or Aerogal. My last trips there in 2005 and 2007 were with Aerogal.
They both fly single aisle planes: Aerogal flies 737s; I don't remember what TAME used to fly since I haven't flown them on recent trips.
Yes, there are weight restrictions. Aerogal's website lists the allowances as 20kg for checked luggage and 10kg for 1 piece of carry-on.
My experience with Aerogal has been much better than with TAME - we did not have to pay for excess luggage on my last two trips. I attribute that to the work of the local agents who act on behalf of the liveaboard to coordinate airport transfers, hotel check-ins, and in this case, group check-ins. I would imagine that Peter Hughes has similar arrangements with a local agent to assist their customers.
I haven't had problems with the luggage not arriving with me in 4 trips there.
Baggage claim at either Baltra or San Cristobal airports in the Galapagos was a bit haphazard so making your bags stand out for easy recognition helps. As of my last trip there, there was no conveyor as you might have grown used to. When the luggage is unloaded from the plane, it is wheeled to a holding area where they are piled on the floor. Then the passengers from that flight are allowed to come in to pick out their bags. Then they check to match up the luggage tags against the luggage stubs.
