"short, thick piece" of something, 1690s, probably a nasalized variant of chuck (n.1) "cut of meat;" meaning "large amount" is 1883, American English. Meaning "person or beast that is small but thick-set and strong" is from 1822.
"a stick or staff used in beating, a war-club, staff used to strike the ball in certain games," c. 1200, from rare Old English batt "cudgel," a western England word at first, probably from Welsh or another Celtic source (compare Irish and Gaelic bat, bata "staff, cudgel"), later reinforced and influenced by Old French batte "pestle," from Late Latin battre "to beat;" all from PIE root *bhat- "to strike." As a kind of wooden paddle used to play cricket (later baseball), it is attested from 1706.
Middle English sense of "a lump, piece, chunk" (mid-14c.) was used of bread, clay, wool, and survives in brickbat and batting (n.1). Phrase right off the bat (1866), also hot from the bat (1870), probably represent a baseball metaphor, but cricket or some other use of a bat might as easily be the source--there is an early citation from Australia (in an article about slang): "Well, it is a vice you'd better get rid of then. Refined conversation is a mark of culture. Let me hear that kid use slang again, and I'll give it to him right off the bat. I'll wipe up the floor with him. I'll ---" ["The Australian Journal," November 1888].
suffix forming almost all Modern English plural nouns, gradually extended in Middle English from Old English -as, the nominative plural and accusative plural ending of certain "strong" masculine nouns (such as dæg "day," nominative/accusative plural dagas "days"). The commonest Germanic declension, traceable back to the original PIE inflection system, it is also the source of the Dutch -s plurals and (by rhotacism) Scandinavian -r plurals (such as Swedish dagar).
Much more uniform today than originally; Old English also had a numerous category of "weak" nouns that formed their plurals in -an, and other strong nouns that formed plurals with -u. Quirk and Wrenn, in their Old English grammar, estimate that 45 percent of the nouns a student will encounter will be masculine, nearly four-fifths of them with genitive singular -es and nominative/accusative plural in -as. Less than half, but still the largest chunk.
The triumphs of -'s possessives and -s plurals represent common patterns in language: using only a handful of suffixes to do many jobs (such as -ing), and the most common variant squeezing out the competition. To further muddy the waters, it's been extended in slang since 1936 to singulars (such as ducks,sweets,babes) as an affectionate or diminutive suffix.
Old English single-syllable collectives (sheep, folk) as well as weights, measures, and units of time did not use -s. The use of it in these cases began in Middle English, but the older custom is preserved in many traditional dialects (ten pound of butter; more than seven year ago; etc.).