It is clearly a
Dutch and Low
German diminutive of a name beginning in
May- (or
Mai-,
Mei-, Mey-, Mij-,...all pronounced the same). Spelling wasn't normalised at that time, specially the diphthong ei can have many forms. Besides the obvious
Maria, the source name can also be derived from the Germanic name element Megin- "big, great", such as Meinhild.
--elbowin