Hi!
Most are certificated at 1999 kg which has an impact on landing fees and avoid Nav charges airways.
Yes, and that's the only real problem of this aircraft (apart from being a Seneca, but that's another story). I used to fly a well equipped Seneca V (former Lufthansa training aircraft) with long range tanks that had been re-registered in the "below 2000kg" class. With full tanks it had 24lb of payload left, pilot included. So either a chimpanzee had to fly it or you were illegal for the first hour of flight...
If you buy one, never ever under no circumstances whatsoever let anyone else fly it. There are two kinds of Senecas: Those who already had their landing accident(s) and those with the accident waiting to happen. (The Seneca V I used to fly was almost written off after some guy bounced on landing and hammered the gear into the aircraft instead of going around...)
Happy landings
max