The kid eating alone might be fine. The kid eating alone might not be. Asking once costs you nothing.

You cannot tell from across a room which kind of alone somebody is having. Some are perfectly content and some are having a bad week, and both look identical from a distance, which makes guessing a poor substitute for asking. Asking carries almost no risk for you: a short answer, a shrug, maybe a conversation. The cost of saying nothing is carried by somebody else.

Ask once this week, lightly, and leave the door open rather than pushing it. Mind if I sit here, or a hello by name, is enough. If they would rather be left alone, let that be fine, since you are offering rather than rescuing.