I don't know why I said DEL, my tickets are through BOM instead this time. Yep, domestic connection from BOM. I remember DEL having a separate area that's just for rechecking in bags, maybe BOM has something similar?

Right, I am connecting from North America but had a stopover in Singapore, so now I would be checking in again at SIN so am quite hopeful.

UPDATE: Worked out fine, SQ was able to tag through and get me a boarding pass for both flights at SIN.
At BOM, the transfer desks were closed so I had to go back to departures and wait for the domestic desk to open, should have gone to the arrivals lounge instead.
BOM check in agent did not question the weight of the bags at all, she saw that they were tagged through and just accepted them.