1861, originally of ships; probably a back-formation from stability, or else from French stabiliser. Related: Stabilized; stabilizing. Earlier verbs in the same sense were stabilitate (1640s) and simple stable (v.) "make steady or firm, make stable" (c. 1300), from Old French establir.
stabilize prices
The drug stabilized her blood pressure
The economy stabilized
*sta-
stab
Stabat Mater
stability
stabilization
stabilize
stabilizer
stable
stable-boy
staccato
stack