A small worker given a narrow stage — the browser's word for tiny scripts running close to the metal, as in audio's realtime lane.
Old English weorc (work, labor) plus the diminutive suffix -let (from Old French -el and -et, the same ending as booklet and ringlet); a worklet is literally "a small work" — a piece of code cut down to run inside a narrow stage built just for it, as in the Web Audio API's AudioWorklet.
A script cut down to one job and run close to the machine, without the weight of anything larger around it. The diminutive in the name is exact — sized on purpose to the single task it was built for, and asked to do nothing past that task.