As happy as Larry simply means very happy.
It is originally an Australian expression but has certainly been commonly used in the UK throughout my lifetime.
Its origins are alleged to lie with a noted boxer called Larry Foley (1847-1917). Foley was a successful pugilist who never lost a fight. He retired at 32 and collected a purse of £1,000 for his final fight. So, we can expect that he was known to be happy with his lot in the 1870s - just when the phrase is first cited.
The earliest printed reference currently known is from the New Zealand writer G. L. Meredith, dating from around 1875:
"We would be as happy as Larry if it were not for the rats".
Alternatively, the word may actually relate to a larrikin, an Australian term for a particular type of ruffian who flourished in the 1880s and who were disposed to larking about. Larrikins had their own style of dress recognisable by its excessive neatness and severe colours.
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