Maintain
Middle English (also in the sense ‘practise an action habitually’): from Old French maintenir, from Latin manu tenere ‘hold in the hand’.
wiktionary
From Middle English mayntenen, from Old French maintenir, from Late Latin manūteneō, manūtenēre(“I support”), from Latin manū(“with the hand”) + teneō(“I hold”).
etymonline
maintain (v.)
c. 1300, maintenen, "to support, uphold, aid;" also "hold fast, keep in possession, preserve from capture or loss," from Anglo-French meintenir (Old French maintenir, 12c.) "keep (a wife), sustain; persevere in, practice continually," from Latin manu tenere "hold in the hand," from manu, ablative of manus "hand" (from PIE root *man- (2) "hand") + tenere "to hold," from PIE root *ten- "to stretch."
Sense of "hold in an existing state or condition, keep in existence or continuance" is from early 14c. Meaning "to carry on, keep up" is from mid-14c.; that of "to keep oneself, support" is from late 14c. Sense of "defend in speech, uphold by argument or assertion" is from mid-14c. Meaning "practice habitually" is from c. 1400. Sense of "furnish means for the subsistence or existence of" is from c. 1400. Related: Maintained; maintaining; maintains.