You have many blockers to strong hands, you can't win by checking, flushes missed, the person calling three times and checking on the river doesn't represent strong holdings, and things like calling with second or third pair is hard after three bets.
Let's thing about this hands from a range perspective. The BB can have a huge defend range, but hands they would raise with haven't done so yet. I think we can discount a lot of strong holdings like pocket pairs above 66s, things like AJs,ATo,KJs,KQo,etc. Of course they can have them everynow and then but they should be raising with them up until this point. Again I know you're looking at Upswing and I've linked an article below that explains this with the ranges.
Essentially the opponents range can't really be good as they've not shown any indication of it being strong so far. Yes they've called every bet so far, but they've also checked the river. You cannot win by checking back. The way the BB has played this hand really indicates their range is something like a missed flush, straight draw or a pair of sixes or maybe a seven. Betting puts pressure and tells a convincing story. Think about how many times you've seen people triple barrel bluff, it's rare and you put an immense amount of pressure on very weak holdings. There are just better spots for this person to play so they should just fold. Of course this depends on the player of course.
Article on this