] ] I read it as Henry almost acknowledging his intentions towards Catherine, and Eleanor, knowing (possibly by Henry’s prior confession to her) how much he likes Catherine, is teasing him.

] I had a bit different take on this, and rather than repeat myslf, I'll link to it below. ;-)
From Cheryl's previous post:
"But it also shows that Henry has plans to be in Catherine's company in the future, else how can he promise that she will be better acquainted with his "odd ways"? This is significant, no? ;-) "

Well, reading this and a few other posts that I missed before – I am toying now with yet another variation of Henry’s intentions:
We see Henry seeking, teasing, liking Catherine. But we also see Eleanor seeking Catherine, encouraging her and altogether very agreeable towards her.
How should we understand her behavior? She knows about Catherine’s feeling toward Henry.( And we suspect that she included Henry in her observation.)
It would be very rude and unkind of both brother & sister to encourage thus Catherine. It would be almost Isabella like, unless..
..Unless Henry’s intentions are real, and known to his sister.
Could he have come to Bath in search of a wife? If that is the case, his marriage/dance conversation would be seen more in earnest.
Would an eligible, honorable man even mention marriage to a pretty eligible young girl if his intentions are not for real?