Thanks again. The withdrawal is now showing up and has 8 confirmations, but Weaver isn't showing any balance. I'll continue to wait, but once it's in my wallet should I be able to send coins out to Silk Core?
No Weaver swaps to SLK are being processed in the next 24-48 hours, after which you'll be able to withdraw to Silk Core.
A lot of this stuff's already been asked by others, if you check SilkNetwork's
post history there's a good chance there will be an answer within the last few posts. The OP is also full of useful info.