According to the '04 Chevy Silverado brochure:
GVWR for an Ext cab, long box and an ext cab short box is 9200.
Payload for 2wd, ext cab, long box is 3644
Payload for 4wd, ext cab, long box is 3372
Payload for 2wd, ext cab, short box is 3798
Payload for 4wd, ext cab, short box is 3569
Subtract payload from GVWR and you will have an approximate of the truck
Weighing it will, of course, give the most accurate answer. I know that a
local moving and storage company has a scale but I've never asked them about
the public using it.
Hope this is helpful.