"Asking would be needy"
The check is the obvious answer, and there's a reason you don't do it. Asking seems needy. "Is everything all right?" sounds like a person who needs reassurance. "Was there a problem with the report?" sounds like a person who can't take two lines without falling apart. Better to sit with it than to show it.
Two things. The first is a study that's been used in earlier books in this series and applies here. Kenneth Savitsky, Nicholas Epley and Thomas Gilovich, in 2001, found that people expect to be judged much more harshly for their slips and awkward moments than observers actually judge them. The fear of looking needy is one of those forecasts. From the inside, "you seem quiet, is everything all right?" is an exposure. From the outside, it's a kind sentence that most people are glad to hear, and that the tired person at the dinner table will usually answer with the day behind it, and a little gratefully.
The second is what the check is and isn't. It isn't "are you angry with me?", which puts you at the centre again and asks them to manage your reading. It's a question about them. "You seem quiet tonight." "Was that a rough one at work?" "Just checking Thursday's a normal catch-up and not about the report?" One sentence, plain, aimed at their day and not at your standing. That's not needy. It's the noticing from chapter 9, said out loud, and it's the single most useful thing a person who notices moods can do with what they've noticed.
There is a version of asking that is what you're afraid of, and it's worth naming. Asking the same question every evening, or asking for a verdict on yourself, or asking in a way that requires a long reassurance before you'll believe it. That's reassurance seeking, and it wears people down, and it's a different habit with its own logic. The check isn't that. The check is asked once, about them, and the answer is accepted. If the answer is "I'm fine, just tired", that's the end of it, and the evening is yours again.