increase payload capacity 2004 Suburban 1/2 ton

Air bags or Supersprings or Timbrens will give suspension better ability to carry more payload and as one poster suggested a LT C or D tire will help also as long as the wheel can use the higher pressures.

A gear change doesn't affect load carrying ability but just better towing performance/higher tow ratings.

Your call on upgrading to a 250 truck.