My late MIL used to turn every offer of a cup of tea or a biscuit or sandwich into a major performance. Just half a cup/ half a biscuit / a quarter of a sandwich not a drop or crumb more because 'I can't manage any more than half a cup yada yada yada...' Everyone knew she had a small appetite so we automatically gave her tiny portions — but if you were foolish enough to ask her if she'd like something to eat or drink you'd get the full performance. And once you delivered the tea/ biscuit/ sandwich there'd be a cheery telling-off. 'Oooh, this is far too much. Call this half a cup? I could drown in this sea of tea...' So no matter what you did with the intention of being kind and supportive, you were always in the wrong.
It irritated everyone, even though her family all loved her to bits. This evening I offered my DP some leftover apple crumble and got the full MIL treatment. 'Just a tiny bit: think half of what you'd have and then halve that. And don't go drowning it in custard, I know what you're like with custard...' So I served a teaspoonful of apple crumble in an eggcup with a tiny blob of custard and as I set it down in front of DP I said jokingly 'You're turning into your mother!' Cue a huge row about me insulting the sacred memory of MIL and doors slamming.
What's the half-cup-of-tea things really about? I have no problem at all with someone saying they're not very hungry, they'll just have a mouthful of whatever. Or a small cup of tea. But there's a point at which it slips into controlling behaviour. Or AIBU?
PS Perhaps I should add that my DP isn't on a diet or anything.