formerly also accrew, mid-15c., "to fall to someone as an addition or increment," of property, etc., from Old French acreue "growth, increase, what has grown," fem. of acreu, past participle of acreistre (Modern French accroître) "to increase," from Latin accrescere "grow progressively, increase, become greater," from ad "to" (see ad-) + crescere "grow" (from PIE root *ker- (2) "to grow"). Related: Accrued; accruing.
Apparently an English verb from a French noun because there is no English noun to go with it until much later (the earliest seems to be now-obsolete accrue, 1570s), unless the record is defective. From late 15c. as "happen or result as a natural growth;" from 1881 as "gain by increment, accumulate." Alternative verb accrete "grow by adhesion" (1784) is rare, as is accresce (1630s), from Latin accrescere.
suffix forming nouns of action from verbs, mostly from Latin and French, meaning "act of ______ing" (such as survival, referral), Middle English -aille, from French feminine singular -aille, from Latin -alia, neuter plural of adjective suffix -alis, also used in English as a noun suffix. Nativized in English and used with Germanic verbs (as in bestowal, betrothal).
1610s, "act of growing by organic enlargement;" 1650s as "that which is formed by continued growth from without," from Latin accretionem (nominative accretio) "an increasing, a growing larger" (as of the waxing moon), noun of action from past-participle stem of accrescere "grow progressively, increase, become greater," from ad "to" (see ad-) + crescere "grow" (from PIE root *ker- (2) "to grow"). It goes with the verb accrue. Related: Accretional; accretionary.