Let  be the modulation space with parameters p, q and weight function ω0. If ∂αa/ω ∈ L∞ for all α, then we prove that the pseudo-differential operator at(x, D) is continuous from  to . More generally, if 𝔅 is a translation invariant BF-space, then we prove that at(x, D) is continuous from M(ω0ω)(𝔅) to M(ω0)(𝔅). We use these results to establish identifications between such spaces with different weights.