Thanks, Andrew. I had tried clipping the weighting raster as well, and had similar issues.
The plot thickens: On a few of my attempts, I cancelled the operation. In most cases, my cancellation resulted in an ArcMap crash (further fueling my frustration!). However, on two occasions, the cancellation actually finished, and then output the weighted flow accumulation. The output raster in these cases were the full project extent with correct values (i.e. exactly the output I was hoping for). This all tells me that the flow accumulation operation is somehow stalling out, and continuing to run unnecessarily. Unfortunately, this whole process of having to cancel to get the right output is extremely inefficient, especially considering that I have to run the operation 50 or so times (and was hoping to batch process or iterate in Model Builder).
Has anyone experienced similar issues, or have any possible solutions about my problem. My next solution is to try running this on another computer with a different version of ArcMap.
Thanks for any help in advance.
Nick