I think that this is the closest we get to a Bagginshield-becoming-canon moment. Because Balin knows. And if Balin knows, I'm willing to bet every bit of money I have that the rest of the Company did too. Because for all of their roughness and seeming lack of civility, dwarves are an observant bunch. They often choose not to say anything, because they don't like to interfere with other people's affairs, but they knew. They saw the bond between their King and their Burglar, because how could anyone not see it?
The way Balin's looking at Bilbo, the slight smile that's both happy and unbearably sad at the same time...it's because he sees what could have been. He looks into Bilbo's eyes as he tries to put his feelings for Thorin into words, and he keeps on smiling despite Bilbo not making any sense. The hobbit's lack of coherency speaks more strongly than any pretty words ever could.
Balin even ducks his head a little when Bilbo's trying to say what Thorin was, his eyes softening in a way that just screams: "I know, lad. I know."
He knows that Thorin was Bilbo's. Just as Bilbo was Thorin's. Two halves of a whole.
But Balin doesn't say any of that, because that would also be acknowledging that Bilbo's love is gone, and with it the chance for something beautiful. Bilbo knows it, you can see it in that brief, painful smile he gives Balin before departing.
Saying it out loud would make it somehow more real, and so Balin's look and Bilbo's smile are the only acknowledgements of an unspoken truth, a heartbreaking realization that even a love as strong as Bilbo and Thorin's wasn't strong enough to fight fate, wasn't strong enough to keep them together.
BAGGINSHIELD: The ship that's impossible not to ship, even though it makes you question everything good in the world and results in an inhumane amount of feelings.
Now if you'll please excuse me, I have a bathtub to fill with my bitter tears.
