I didn't have a BT Cruiser, but I used to own a Gulfstream motorhome on a 14,050 GVWR Ford Chassis. It's towing capacity was 3,500 pounds per Gulfstream, which was limited by the hitch. The actual chassis towing capacity was higher, since the GCWR (Gross Combined Weight Rating) of the chassis was 20,000. I never towed more than 3,500 pounds with the motorhome so I didn't worry about it. IIRC the GCWR of the Chevy chassis with the 6.0 and 4.10 rear axle in that year was 16,000 (at least it was on my 2005 Silverado). This would limit you to towing just over 3500 pounds.
2017 VW Golf Alltrack
2000 Ford F250 7.3