late Old English flotian "to rest on the surface of water" (intransitive; class II strong verb; past tense fleat, past participle floten), from Proto-Germanic *flotan "to float" (source also of Old Norse flota, Middle Dutch vloten, Old High German flozzan, German flössen), from PIE *plud-, extended form of root *pleu- "to flow."
Meaning "drift about, hover passively" is from c. 1300. Transitive sense of "to lift up, cause to float" (of water, etc.) is from c. 1600; that of "set (something) afloat" is from 1778 (originally of financial operations). Of motion through air, from 1630s. Meaning "hover dimly before the eyes" is from 1775. Related: Floated; floating. A floating rib (by 1802) is so called because the anterior ends are not connected to the rest.