Hi, as you say, your sources aren't strong , they could be if the genealogist had supplied references. Nevertheless, they are a very good guide to your own research. It's much more fun that way, anyway.
There is a general guide to reliable sources here https://www.wikitree.com/wiki/Space:England_Project_Reliable_Sources
The England Project does have a scheme in place which helps people learn how to find and record English records.
The parish registers for Kettering from 1710 and for Warkton from 1550 are available to view on ancestry (possibly on FMP also but of course they both charge) There is an index/transcription of both of them on Free Reg.
They record a marriage in 1711 of Thomas and Mary in Kettering and one in 1712 in Warkton of a Thomas Page to Elizabeth Smith but on the second marriage, the transcriber says that the bride, is described 'of Kettering'
Edit: I've just checked the original and the Bishop's transcript. (on Ancestry)
The Bishop's transcript is vague, it says Thomas Page and Eliz Smyth of Kettering were married.
The original says 'Thomas Page and Elizabeth Page,both of the parish of Kettering
But there is still a possible problem (I checked in the original as well as on Freereg this time !
There are 3 baptisms of children of a Thomas Page, in Kettering in 1813, One is of Thomas son of Thomas and Elizabeth in April but the other two are children of Thomas and Mary baptised in November.
Link to the search page on Free reg https://www.freereg.org.uk/search_queries/new?locale=en
I'm not sure how you would confirm that this Thomas Page was the innkeeper at the George. A search of the Northamptonshire Archives (they have an online catalogue) might help. There may be a directory but this is quite an early date) I did find that the innkeeper in 1733 was a man called Thomas Dawson https://www.british-history.ac.uk/vch/northants/vol3/pp218-226