"They'll think I'm tight"

This is the fear at the bottom of the split, and it has a specific picture in it. You decline the second bottle, or ask to pay for what you had, and the table exchanges a look, and from then on you're the tight one.

Kenneth Savitsky, Nicholas Epley and Thomas Gilovich, in 2001, ran studies on how people expect to be judged after small failures and awkward moments, and compared that with how observers actually judged them. The people in the awkward moment expected far harsher judgement than the observers gave. Observers barely registered what the actors were sure would define them. This study has been used in earlier books in this series because it applies to so many social fears, and it applies here. The forecast that the table will think you're tight is made by you, from inside the awkward moment, and forecasts made from there run harsh.

What does the table actually think when someone says "I'll just pay for mine, if that's all right"? In my experience, three things, in this order. Nothing, because they're looking at their own share. Mild relief, from the two or three people who had a main and a glass and were about to pay for the fish. And, occasionally, a flicker of irritation from the person who ordered the fish, which lasts as long as it takes to work out the new number. Nobody files it. Nobody remembers it in a week. The picture of the exchanged look is the picture the forecast paints, and it's the picture Savitsky's actors painted, and it was wrong.

There's a longer-term version of the fear, that repeated quiet no's add up to a reputation. I'd say two things. The first is that reputations for tightness are earned by people who are tight with others, not with themselves. The person who never buys a round, who forgets their wallet, who lets others pay, is tight. The person who orders what they want and pays for what they had is ordinary. The second is chapter 6's point. Half the table is doing the same sums you are, and the person who says the number out loud is the one they'll be grateful to.

Say it once, plainly, and watch what happens on the faces rather than in the forecast. The evidence says the faces are where the truth is.