“Yeah, I finished the chips” is a small sentence that builds a big reputation.

Owning something trivial when nobody would ever have caught you is the cheapest possible proof that you tell the truth. People notice it more than they let on, and they extrapolate, since anyone straight about the snacks is probably straight about the rest. The size of the admission has almost nothing to do with the size of what it demonstrates.

Next time you could quietly let a small thing pass, say it instead. Keep it plain, with no apology and no explanation attached. A few rounds of that make the larger admissions far less frightening.