While we are on the subject of thinking seriously, Anne's reflection on Mr Elliott is interesting:

She saw that there had been bad habits: that Sunday travelling had been a common thing; that there had been a period of his life (and probably not a short one) when he had been, at least, careless on all serious matters; (Ch.17)

As well as the more general meaning, the expressions 'thinking seriously' and 'serious subjects' had a specific meaning associated with religious and moral matters. Edmund uses the expressions in his conversation with Mary in the Chapel at Sotherton. (MP Ch.9) In the quote above the example of Sunday travelling is a shorthand way of implying general laxity in matters of religion and Sunday observance.

A post by Julie W in the L&T Archives about Sunday observance is here:

http://www.pemberley.com/bin/library/ppgr2004.cgi?read=580

Another post about Sunday travelling is linked below.

I'd hazard a guess that Anne, her mother and Lady Russell did think 'seriously' and not only on Sundays, whilst Sir Walter and Elizabeth observed the Sabbath because it was the 'done thing' but spent the day thinking seriously about their hairdos or their next dinner party.