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"confoundedly" 1833, later also as an adjective, from past participle of blame (v.), as a "euphemistic evasion of the horrible word damn." [Bartlett, "Dictionary of Americanisms," 1848].
This adjective 'blamed' is the virtuous oath by which simple people, who are improving their habits, cure themselves of a stronger epithet. [Edward Everett Hale, "If, Yes, and Perhaps," 1868]Cf. also blamenation (1837) as an expletive. The imprecation blame me is attested from 1830.
c.1200, "find fault with;" c.1300, "lay blame on," from Old French blasmer (12c., Modern French blâmer) "to rebuke, reprimand, condemn, criticize," from Vulgar Latin *blastemare, from Late Latin blasphemare "revile, reproach" (see blaspheme). Replaced Old English witan with long "i." Related: Blamed; blaming.
early 13c., from Old French blasme "blame, reproach; condemnation," a back-formation from blasmer (see blame (v.)).