Resource-bounded strong dimension versus resource-bounded category

Classically it is known that any set with packing dimension less than 1 is meager in the sense of Baire category. We establish a resource-bounded extension: if a class X has Δ-strong dimension less than 1, then X is Δ-meager. This has the applications of explaining some of Lutz's simultaneous Δ-meager, Δ-measure 0 results and providing a new proof of a Gu's strong dimension result on infinitely-often classes.