Etymology
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-happy 
word-forming element used in World War II armed forces slang and after, meaning "crazed or frazzled from stress due to" the thing specified (as in bomb-happy (1942), flak-happy (1943), trigger-happy (1942). The model might have been slap-happy in pugilism from 1936 as a slang variant of "punch-drunk."
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-y (3)
suffix in pet proper names (such as Johnny, Kitty), first recorded in Scottish c. 1400; according to OED it became frequent in English 15c.-16c. Extension to surnames seems to date from c. 1940. Use with common nouns seems to have begun in Scottish with laddie (1546) and become popular in English due to Burns' poems, but the same formation appears to be represented much earlier in baby and puppy.
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-ment 

common suffix of Latin origin forming nouns, originally from French and representing Latin -mentum, which was added to verb stems to make nouns indicating the result or product of the action of the verb or the means or instrument of the action. In Vulgar Latin and Old French it came to be used as a formative in nouns of action. French inserts an -e- between the verbal root and the suffix (as in commenc-e-ment from commenc-er; with verbs in ir, -i- is inserted instead (as in sent-i-ment from sentir).

Used with English verb stems from 16c. (for example amazement, betterment, merriment, the last of which also illustrates the habit of turning -y to -i- before this suffix).

The stems to which -ment is normally appended are those of verbs; freaks like oddment & funniment should not be made a precedent of; they are themselves due to misconception of merriment, which is not from the adjective, but from an obsolete verb merry to rejoice. [Fowler]
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-ty (1)
suffix representing "ten" in cardinal numbers that are multiples of 10 (sixty, seventy, etc.), from Old English -tig, from a Germanic root (cognates: Old Saxon, Dutch -tig, Old Frisian -tich, Old Norse -tigr, Old High German -zug, German -zig) that existed as a distinct word in Gothic (tigjus) and Old Norse (tigir) meaning "tens, decades." Compare tithe (n.).

English, like many other Germanic languages, retains traces of a base-12 number system. The most obvious instance is eleven and twelve which ought to be the first two numbers of the "teens" series. Their Old English forms, enleofan and twel(eo)f(an), are more transparent: "leave one" and "leave two."

Old English also had hund endleofantig for "110" and hund twelftig for "120." One hundred was hund teantig. The -tig formation ran through 12 cycles, and could have bequeathed us numbers *eleventy ("110") and *twelfty ("120") had it endured, but already during the Anglo-Saxon period it was being obscured.

Old Norse used hundrað for "120" and þusend for "1,200." Tvauhundrað was "240" and þriuhundrað was "360." Older Germanic legal texts distinguished a "common hundred" (100) from a "great hundred" (120). This duodecimal system is "perhaps due to contact with Babylonia" [Lass, "Old English"].
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