Clutch,
Welcome to the forum. Let's see if I can word this right for you.
D1.1, according to section (now "Clause" in the 08 edition) 1, deals with material from 3/16 and up. So the fillet weld sizes are more than likely called out accordingly. D1.3, which can be used in conjunction with D1.1, deals with thinner materials.
Also, different codes do call things differently. That is why a CWI must be very careful as to which code (i.e. D1.1, API 1104, ASME, etc.) the engineers are calling the work to be completed to and then inspected to. We are taught not to memorize material but to always refer to the code in use at the time.
Next, the engineer is always free to modify anything to his own specific uses apart from the code. If the stamped prints call out weld 'X' then that is what had better be in the spot he called it out. Not what I think, or even what the code says. He is the man with ultimate power, knowledge, and final say as to application.
Hope that answers your question satisfactorily. Have a Great Day, Brent