I am curious why, as suggested above, a larger unit would run too infrequently and thus be unsuccessful at removing the humidity. My neighbor (1700 Sq ft, 1 story) replaced his 2 ton unit with a 3 ton unit and said it does a much better job of maintaining temperature and removing humidity.
I'll try to answer a few of your questions.
A 3 ton is a 3 ton no matter the age or refrigerant used.
If there is any difference, you may not be running at full capacity due to its age.
The difference between your house and the neighbors is the second story.
You have part of the house with cooled space above.... you have less heat gain.
Units are sized by sq ft, insulation values and design temp. Maybe some other thing I have forgotten, I'm not an engineer.
A simple HVAC as described is either on or off.
It only works at one speed.
If it is hotter outside, the compressor will have higher pressures and pull more amps.
A HVAC does not "cool" the air, it removes heat. The hotter it is outside, the harder it is to get rid of the heat gathered.
Heat pups have to gather heat from outside and bring it in. That is why they are less effective in colder climates.
Temperature setpoint or humidity have no effect on how hard a HVAC works.....just how long it runs.
Your unit does not "know" what the temperature is...it is either on or off as controlled by the TStat.
Unless a humidistat has been added...humidity has no effect on run time.
A properly sized unit will run long enough to control humidity.
Some engineers will oversize the evaporator coils in humid areas by 1/2 ton just for the extra surface area.
Allows for more condensate to form and run off.
An oversized unit may not have enough runtime to allow enough condensate to form and run off the coil to the drain.
I have had buildings that had drastically oversized units. They did not run long enough for the condensate to run off the coil.
In those cases, the condensate just evaporated and re-entered the space.
The air exiting the evaporator coil is at 100% humidity.
When that air warms and expands the humidity lowers.
Undersized units or undercharged units do not form condensate well.
The evap coil is not getting cold enough.
As a simple rule of thumb, your suction line should have condensate on it all the way back to the compressor...but not on the compressor body.
The best way to run a system in cooling mode is fan on.
It keeps interior temperatures more even and prevents hot spots.
Acts like a ceiling fan. The extra run time us somewhat offset by the lack of starting amps from the start stop of "Auto" operation.
A utility company class I took long ago said it was cheaper to run the fan all the time.
That may have changed.
In Heat mode, fan on auto.
