"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.