Me is used in many constructions where strict grammarians prescribe I. This usage is not so much ungrammatical as indicative of the shrinking range of the nominative form: me began to replace I sometime around the 16th century largely because of the pressure of word order. I is now chiefly used as the subject of an immediately following verb. Me occurs in every other position: absolutely <who, me?>, emphatically <me too>, and after prepositions, conjunctions, and verbs, including be<come with me><you're as big as me><it's me>. Almost all usage books recognize the legitimacy of me in these positions, especially in speech; some recommend I in formal and especially written contexts after be and after as and than when the first term of the comparison is the subject of a verb.
Origin of ME
Middle English, from Old English mē; akin to Old High German mīh me, Latin me, Greek me, Sanskrit mā