You can be unable to help and still be considerate in how you say so.

A refusal carries two separate pieces of news, and people tend to conflate them. There is the fact that the help is not coming, which cannot be softened, and there is what the other person hears about their standing with you, which is entirely in your hands. Rushed or vague answers leave them guessing about the second one, so a practical disappointment turns into a question about the relationship.

When you cannot do something this week, say so early and clearly, and add one honest sentence about wishing you could. If there is a smaller thing you can manage, name that rather than leaving the door ambiguous.