It's possible the a/c compressor is seized up. Most of the time the belt will just burn up and break, but if the belt holds on it can be a big enough load to stall the engine. Please call Scot or myself at 972-420-6187 and we'll be happy to help you find the solution.
RepairPal Certified shops can diagnose and repair your 2003 Chevrolet Suburban 1500. They provide transparent pricing with a minimum 12-month or 12,000-mile warranty on repairs and services.