Reminds me of the character Weaver in
A Gathering Light. It's a positive connotation but I don't really like it outside of that character. It's a bit in-your-face occupation (although not as in-your-face as Engineer or Architect, haha) and I'm not really into that.
I would definitely rather see it on a male. I don't like Waverly at all, but
Webster is okay.
I think Weaver would be a fine MN. It would be quite handsome next to something classic like
Thomas Weaver or
Henry Weaver.
Also, I was thinking about teasing potential. Wiener, Beaver... man you could rip a Weaver to shreds, if you were so inclined... :P