generally (adv.)

c. 1200, "of wide application, generic, affecting or involving all" (as opposed to special or specific), from Old French general (12c.) and directly from Latin generalis "relating to all, of a whole class, generic" (contrasted with specialis), from genus (genitive generis) "stock, kind" (from PIE root *gene- "give birth, beget," with derivatives referring to procreation and familial and tribal groups).

What is common is of frequent occurrence. What is general admits of comparatively few exceptions: the general opinion (the opinion of the majority); the general welfare. [J.H.A. Günther, "English Synonyms Explained & Illustrated," Groningen, Netherlands, 1904]

Used in forming titles from late 14c. with the sense "having general authority or jurisdiction, chief." Phrase in general "without exception, in one body; as a rule, generally, not specifically" is from late 14c. General rule, one applying to an art or science as a whole, is from c. 1400. General store attested by 1810, American English, in reference to the range of goods sold; a general hospital (1737) is one not restricted to one class of persons or type of disease.

common adverbial suffix, forming from adjectives adverbs signifying "in a manner denoted by" the adjective, Middle English, from Old English -lice, from Proto-Germanic *-liko- (cognates: Old Frisian -like, Old Saxon -liko, Dutch -lijk, Old High German -licho, German -lich, Old Norse -liga, Gothic -leiko); see -ly (1). Cognate with lich, and identical with like (adj.).

Weekley notes as "curious" that Germanic uses a word essentially meaning "body" for the adverbial formation, while Romanic uses one meaning "mind" (as in French constamment from Latin constanti mente). The modern English form emerged in late Middle English, probably from influence of Old Norse -liga.