“I can’t this weekend” doesn’t make you a bad friend. Saying yes and resenting it might.

A plain no protects the friendship more than a reluctant yes does. Turning up resentful means your friend gets a worse version of you and does not know why, and they would almost always rather have had the honest answer two days earlier. Capacity is not a character flaw. You have a finite number of Saturdays and other people have claims on them.

Say it early, say it without a story, and do not pad it with fake conflicts. Then offer an alternative if you want to: next weekend, or Tuesday, or something smaller. People remember being told the truth about availability more fondly than they remember a grudging appearance.