I don't see how you describe is even possible. What hand holds the vinyl backer down.
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I just rest the side of my right hand on the backer, giving me plenty of articulation range for the x-acto knife in my right hand fingers. Left hand holds the weeded vinyl, and I sort of "snap and wiggle" the vinyl as I go, paying close attention the upcoming letters as they all require a slightly different approach.
The trick to weeding (aside from good cutting) is anticipating which letters are coming up. An "A" will weed different than a "C", etc. I have found it is far better to have the same person that cut the vinyl to weed it, as they will have internalized the copy and can anticipate what's coming up better. Shoving a pile of cut vinyl to someone who has no clue what he or she is weeding results in a slower process and more errors.
Note: I was the slowest weeder in the shop. The other guys were able to just snap the vinyl off in seconds. The downside to their method is they would usually mess up a letter or two in the process, and would have to recut and position them. By that time my vinyl was applied and I was on to the next job.