Front tires on most homeowner tractors are small. The added benefit of filled front tires will be negligible.
Raise the brush hog on sharp turns. Add weight to the bucket if you have FEL and bucket. Add suitcase weights to the front of the tractor. Go into FWD on turns. Slow down on turns.
Look at your overall mowing pattern. Perhaps it can be modified to reduce the number of tight turns.