(I also got a message from @uselessundertalefacts about Papby, so I’ll answer that too.)
Grillby is a fascinating guy, so of course I love pairing him up with our boys.
Grillby is the perfect listener, and Sans has so much weighing on his soul that he’s grateful to have someone to listen and at least pretend to understand his drunken musings. Grillby isn’t the best influence, though; he’s never going to be the one to push Sans to take better care of himself. Not because he doesn’t care, he’s just not a pushy guy. Sans’ choices are his business, as far as he’s concerned. They’re friends with benefits–and maybe under the right circumstances that could grow into something more–but I’m not sure that would be the best for either of them.
Fellby, on the other hand, actively encourages Red’s worst habits. He’s toxic, and Red knows it, but he keeps coming back…because he doesn’t believe he deserves better.
Grillby is the first to start crushing. He admires Papyrus’ energy and enthusiasm–his passion. Papyrus would be oblivious at first, because he’s a little socially awkward (and not half as confident as he pretends) and Grillby is shy. An outside force would be required to get the two of them together, I think. They’re awkward-cute when they do finally start dating, and they take things slow, partly because they’re both too nervous to make the first move.