The widest I've been able to find 6061 flat stock in 3/16" thickness is 4". You can find that at most of the sites people have listed so far. I'll throw
www.metalexpress.com in too.
If you need 7" width, you'll need to upgrade from flat stock to plate and cut it yourself, or order it pre-cut. Metal Express does carry 1/4" x 8" in 6061 flat stock. But it will cost about the same as getting 3/16" plate pre-cut.
The prices on metalexpress.com:
36x4x3/16 Flat - $16
36x8x1/4 Flat - $40
36x7x3/16 Precut Plate - $40
If you do find a place that carries 3/16" x 7" 6061 flat stock, let me know.
EDIT:
www.metalsdepot.com has 3/16" x 6" 6061 flat stock listed.