It is not so much the operational aspects of operating large aircraft, such as 737-800s, Airbus 320s and similar types of aircraft, rather what to do with them after they land. Parking is very limited during certain times of the year.
I have seen a 727-200 in Aspen, it quite a few years ago and it had received special permission for a one time flight. Aspen is currently undergoing changes moving the taxiway farther from the runway to allow B-737 size aircraft operations. The ramp area for parking is also under going massive changes to allow larger aircraft operations. There are plans to lengthen the runway to the south about one more thousand feet.
The current limit is by wingspan not weight, the wingspan limit is for the BBJ, a non-winglet B-737 can operate in Aspen, I have seen at least three different Corporate B-737s, not BBJs in Aspen.
Hope this helps.