Without knowing the dates or the destination of the B6 ticket, it is hard to tell exactly how the entire itinerary is pricing. But this is one of the facts I mentioned on another thread when DL said they won't through-check luggage unless all the segments are on the same ticket. I said that many times it is
possible to include all flights on the same ticket, but often it is not financially
feasible, as you found out.
One of the frequent DL loyalists on the forum took issue with me (and later said we were talking about different issues, which we weren't, but he easily gets confused). Fortunately life on the forum is so much more peaceful for me since I used the 'ignore' feature