‘Let me know if you need anything’ is kind, but it asks the recipient to invent a task, judge what is reasonable and then request help. A concrete offer can make that easier.
Try: ‘I can bring dinner on Thursday if that would help’ or ‘I have half an hour to review the opening section.’ Both describe a real action with a boundary. The other person can accept, decline or suggest a better fit.
Keep the offer separate from taking action. Someone may welcome help with a document but not want you to rewrite it or send it to others. A useful question is: ‘Would you like comments, or should I suggest edits directly?’
If the answer is no, let it remain no. Repeatedly insisting that you know what would help can turn support into another demand.
Offer only what you can realistically provide. A modest task you complete may be more useful than a sweeping promise that creates further uncertainty.
Before helping, identify the action, its limit and the person’s permission. Support works best when it gives them an additional option. It should not quietly transfer ownership of the situation away from the person who is living it.