My impression is JA confines Sir William to virtually one charecteristic; he is comically pre-occupied with having been presented at the St James's.
He likes to remember this distinction and feels it too strongly.
I think Sir William wants to be considered on a par with people of rank and wealth. He politely if ineptly commends Darcy's dancing and loves to bring up the topic of the Court of St James.
Still, I'm willing to see Sir Wiliam's visit to Mr Bingley and giving him the tickets to the Assembly as done out of consideration and courtesy,; as well as a social duty to a new neighbor- this visit was also a social duty for Mr Bennet.
Sir W. seems a harmless, well meaning, cordial sort of chap though somewhat shallow. ;-)

I am also reminded of Sir William Lucas in P&P2 by this picture of Sir Richard Arkwright. Interesting to note the conventions of a portrait of an aristocrat compared to an industrialist or inventor.
Though Sir William may've worn an embroidered fancy waistcoat for his portrait. Capital !