In D1.1 2004, under General WPS Requirements, look at 3.7.2, Width/Depth Pass Limitation, and Figure 3.1. These work in conjunction with Table 3.7 as they apply. Also, the commentary at C3.7.2 may be helpful.
I KEEP HEARING THAT 4 TIMES THE DIAMETER OF THE ROD BEING USED IS MAX WIDTH FOR A WAEVE BEAD. SO A 1/8" ROD WOULD ONLY BE ABLE TO PUT DOWN A 1/2" WIDE WEAVE. IS THERE HEARSAY OR CODE?
AWS D1.1 does not specifically address the max width of a weave. As SWNorris mentioned, there are limitations on the width and depth of an individual bead. Also there could be heat input limitations that have the same end result.
Maximum weave sizes are more often leftover notions from the past practices of old codes. A lot of people remember having to limit the weave but don't know where it came from. There may be some codes the do have the limitations but D1.1 isn't one of them.