My own experience and everything I have read is not to fill the tires, or at least not fill them like they used to. Now this is with farm tractors with AG tires, I don't know how compacts with R-4 tires are affected. I also have 2 tractors at a friends farm that are very close in set-up and weight that I run on a regular basis(2 of many I have run filled and unfilled over the years). The only major difference is one has filled tires the other has cast weight. The cast weight tractor pulls better, and rides much nicer. Most tire MFG and at least Deere don't recommend filling tires anymore. I know in draft applications the tires work much better unfilled. Unfilled tires will flex more and grip the ground better. I don't know if it would make a difference in loader work. As the loader fills the rear in most cases will get lighter. Where in draft (plowing) the rear gets pulled down.
You also don't have to fill the tires fully, you could only fill say 30%-40% and this would lower the weight and still allow some flex.
In cooler weather filled tires seem to ride really rough and take longer to "warm up" and start flexing.
If I could avoid it I would never again fill tires on any of my own equipment. The problem with compact tractors is it seems hard to add as much weight as needed.