"strip of wood (especially used to fasten canvas over ships' hatches)," 1650s, Anglicized variant of baton "a stick, a staff" (see baton). Nautical use attested from 1769. As a verb, "to furnish with battens," attested from 1775; phrase batten down recorded from 1823.
"to improve, to fatten," 1590s, probably representing a dialectal survival of O.N. batna "improve" (cf. O.E. batian, O.Fris. batia, O.H.G. bazen, Goth. gabatnan "to become better, avail, benefit," O.E. bet "better;" cf. also boot (v.)).