just bought wm-f77 off ebay. belt is toast. where can i find replacement? please advise

Have you tried Sony?  If you have a service manual, find the part number and punch it in at the Sony Professional Sevice website.

Partstore.com lists it as Currently out of stock (part 3-325-387-01)...available as a special order only...suits models Sony TCM57/Sony TCM9/Sony WM75/Sony WM-F57/Sony WM-F75/Sony WM-F77/Sony WMF80

supposed to be a 1mm thick belt approx 7.7 inch stretched length X 2 (inside circumference) or 'total CUT length'.

Will help you out if you can't locate one from Sony direct