"Minnie"??? what's that short for?

[Ray T]

So many Minnies - I have a “Minnie Cooper” on my tree! Then, again, I also have a “Frances Barnett”.

[RossGillbanks]

I have Minnie which seems to have been passed down through various generations. however it seems to have originally started as Martha and then a Martha had a daughter in 1850 named Minnie... No idea if Minnie was a nickname for Martha or if this is useless info

[iolaus]

I wonder if she was Minnie just meant that she was named after her mother a 'mini Martha/Mary/Jane/etc'

[Top-of-the-hill]

   Being fairly sure that Minnie was a given name, I have checked the Kent baptisms between 1840 and 1920 on Findmypast. They list 6,824; there is some duplication, but that is a lot of girls baptised Minnie just in one county. And they wouldn't all have been baptised!

[DianaCanada]

I wonder if she was Minnie just meant that she was named after her mother a 'mini Martha/Mary/Jane/etc'

According to etymonline.com, mini as a prefix meaning “small” came into common usage around 1960, derived from miniature.  I would guess the girl’s name was not related to size.
Just guessing here, but Disney probably chose Minnie just because it went well with Mouse and with Mickey, too.