HVAC-R is one of my specialties; I've designed and installed/modified many residential & commercial systems. I would be glad to advise if you wish, either through PM or open forum.
From what you've posted I suspect that there COULD be an airflow restriction or distribution problem with the duct inside the house. This could be due to a dirty evaporator (inside) coil), dirty filter, closed dampers, poorly designed/installed ductwork, blower speed too low, etc..
Also, here in KY the rough rule of thumb for sizing a residential system is one ton A/C per 400 sq ft (450 for heat pumps) floor space. A 4 ton system could be justified for your 1600 sq ft main level. However, for the purpose of CREATURE COMFORT (and this is what air conditioning is all about) a three ton system should suffice very nicely simply because of the increased dehumidification that is attained from the long (or continuous) runtime of the equipment. An 82F space with low humidity can be just as comfortable as a 72F space with high humidity.
Are the occupants of the space actually uncomfortable, or are the occupants dissatisfied that the space temp doesn't attain to the setting of the t-stat?
Also, the human body can feel a 2F temperature change immediately. Example, if entering a 79F room from a 77F room it will immediately be sensed and COULD be construed as discomfort. This would also indicate an air distribution (balancing) problem.
Also, A smaller system that runs continuously (IF everything is in good working order, i.e., adequate airflow, evap & condenser temps, good oil return to the compressor) is not bad for the system, nor does it necessarily equate to higher electric bills for the simple reason of the locked rotor amps (LRA) that larger systems will experience that cycle 4-6 times an hour. The LRA can be 5 times the RLA (run loads amps).
Here is my advise:
Obtain the make/model on inside & outside units, let's check see what you actually have.
Check for airflow restrictions within the air distribution system and temp differences between rooms.
Does the system have return air duct or is it free return?
Measure the main duct coming from the air handler (not the plenum) the main duct (or ducts) coming from the plenum. Example, for a 3 ton system you must have ductwork that will move 1200 cfm air @ .08 - .1” static friction loss (don't worry, I've got a ductulator that computes this). A rectangular duct of 20 x 10 carries 1200 cfm @ .08 static.
[edit to add]
One more check to make; AFTER the system has run for 8-10 minutes into a cooling cycle go to the outside unit and grasp/feel the two refrigerant lines connected to the unit (you'll probably/should have to peel back insulation for the big line). The small line should feel WARM, not hot. The large line should feel COOL (and sweaty), not cold.