ply (v.1) Look up ply at Dictionary.com
"work with, use," late 14c., shortened form of applien "join to, apply" (see apply). The core of this is Latin plicare "to lay, fold, twist," from PIE root *plek- "to plait, twist" (cognates: Greek plekein "to plait, twine," plektos "twisted;" Latin plectere (past participle plexus) "to plait, braid, intertwine;" Old Church Slavonic plesti "to braid, plait, twist;" Gothic flahta "braid;" Old English fleax "cloth made with flax, linen").

Sense of "travel regularly" is first 1803, perhaps from earlier sense "steer a course" (1550s). Related: Plied; plies; plying.
ply (n.) Look up ply at Dictionary.com
"a layer, a fold" 1530s, from Middle French pli "a fold" (13c.), alteration of Old French ploi "fold, pleat, layer" (12c.), verbal noun from ployer (later pleier) "to bend, to fold," from Latin plicare "to fold, lay" see ply (v.1)). This is the ply in plywood.
ply (v.2) Look up ply at Dictionary.com
"to bend," late 14c., plien, from Old French plier, earlier pleier "to fold, bend," from Latin plicare "to lay, fold, twist" (see ply (v.1)). Related: Plied; plies; plying.