You can do it yourself (at a price) by clicking the HVAC-Calc link at the top of the page. It involves determining insulation factors, window factors, and more... Few companies will do them for replacements, but it's certainly a good way to determine you have the proper-size system. Does it cool well on the hottest days? Does it short cycle or long cycles on hot days? 2200 sq. ft. on a 3 ton doesn't sound out of the ordinary for my area, but it varies by area and construction type. Texas can get hot... you say the unit cools well, though.
Really? I never tought about that. It would raise the humidity.
The house I am in now has a brand new trane 3 ton 13 seer unit that I had installed and on really hot days(in the 100's) if I were to set the thermostat to 70 it would probably never reach it until evening. My house is only 1450 sq. feet.