That make's sense. We have had record breaking heat here in Missouri (107ish). My fuel economy, I've noticed has been steadily declining. I averaged about 25MPG when I was in Louisiana, now I've moved up here and now am averaging 15-20 city and highway combined.A slipping belt will affect the performance of your accessories including the A/C, but I doubt it would affect your economy much. Excessive drag from a worn compressor could hurt it, but it probably wouldn't be a huge difference.
Just some food for thought though...
How hot is it where you live? We're having record heat down here in Texas. Temperature has a huge effect on fuel economy. I worked on a research project in college examining this. Even 10 degrees below or above the ideal operating range can have big effect on fuel economy.
Cold air is good for power production because it's more dense, but hurts fuel economy because the denser air requires more fuel for proper combustion. Colder, denser air also creates more aerodynamic drag. Extremely hot temperatures hurt fuel economy as well though. Most vehicles are programed to start adding extra fuel when the intake air temperatures get above a certain point. The richer mixture helps lower combustion temperatures to maintain proper engine temperature and prevent detonation. Having the A/C on makes this worse and not just from the drag of the compressor. All the heat the A/C is pulling out of the cabin is getting dumped right in front of your radiator, further increasing engine and intake air temperatures. In addition, if you do a lot of city driving the hotter air typically requires much more aggressive throttle inputs and RPM's during acceleration to get the vehicle up to speed.
The ideal temperature range varies by vehicle but is usually around 50-80 degrees, give or take 10 degrees each way. The further you get outside of the ideal range for your vehicle the steeper the economy drop off becomes. The difference between 90 degrees and 100 degrees can be over 20% in some vehicles. With the 110 degree heat here, my 2000 Vulcan has dropped from averaging 28ish MPG on the highway to barely 20 MPG. City driving is even worse.
Some data: For 5 years, I drove a loop of 3500 miles every 2 months. These driven in Lin Cont and easy to check mpg. And when we hit I-70 west of Columbus O, to Kansas City MO, the scenery does not change, and it is boring. For something to do, and for curiosity, I checked mileage time and time again. There were 2 things that kicked mileage. Wind and temp/sun.I've noticed that the A/C has been using a lot more gas then normal lately. What could this be? I was thinking it could be the serpentine belt.