Who pays the grading company's fees?
In short: You do, in advance, either directly to the grading company or as a pass-through invoice you pay before the cards ship. I charge only my own flat service fee and never hold your money.
Grading fees and insured shipping are passed through at cost, with no markup, and they are paid before anything ships. My own charge is a separate flat service fee per card, quoted in writing.
I keep your money and mine completely apart for the same reason I keep your cards apart from anything I own: there is never a question about whose it is. The practice does not provide escrow, hold funds or advance money.