Here is a link to a post I made earlier today about them.

Jane Austen mentions them in Sanditon:

When Mr. and Mrs. Parker, therefore, ceased from soliciting a family visit and bounded their views to carrying back one daughter with them, no difficulties were started. lt was general pleasure and consent.

Their invitation was to Miss Charlotte Heywood, a very pleasing young woman of two and twenty, the eldest of the daughters at home and the one who, under her mother's directions, had been particularly useful and obliging to them; who had attended them most and knew them best.

Charlotte was to go: with excellent health, to bathe and be better if she could; to receive every possible pleasure which Sanditon could made to supply by the gratitude of those she went with; and to buy new parasols, new gloves and new brooches for her sisters and herself at the library, which Mr. Parker was anxiously wishing to support.

Chapter 2

THey were places wher one subsribed by paying a yearly fee to borrow books9 and also purchase other friperies :-)...).
Here is a drawing by Cruikshank of the interior of one of these places. I hope you can make out the signs on the bookshelves which read "Romance" and "Novels" ;-)

I think it highly likely that the officers were hanging out at the circulating libraries in Meryton, in order to meet the inhabitants.

JA and her family subscribed to Mrs Martins ill fated circulating library which was in Basingstoke :

I have received a very civil note from Mrs. Martin, requesting my name as a subscriber to her library which opens January 14, and my name, or rather yours, is accordingly given. My mother finds the money. May subscribes too, which I am glad of, but hardly expected. As an inducement to subscribe, Mrs. Martin tells me that her collection is not to consist only of novels, but of every kind of literature, &c. She might have spared this pretension to our family, who are great novel-readers and not ashamed of being so; but it was necessary, I suppose, to the self-consequence of half her subscribers.

Steventon: Tuesday December 18th 1798.

and

Our whole neighbourhood is at present very busy grieving over poor Mrs. Martin, who has totally failed in her business, and had very lately an execution in her house. Her own brother and Mr. Rider are the principal creditors, and they have seized her effects in order to prevent other people's doing it. There has been the same affair going on, we are told, at Wilson's, and my hearing nothing of you makes me apprehensive that you, your fellow travellers, and all your effects, might be seized by the bailiffs when you stopt at the house, and sold altogether for the benefit of the creditors.

8th November 1800