Green’s Dictionary of Slang

fret one’s fat v.

to worry; also as phr. God fret my fat.

[UK]R. Llewellyn None But the Lonely Heart 51: Don’t you fret your fat about me.
[Aus]D. Niland Call Me When the Cross Turns Over (1958) 13: Keep your shirt on, Blue. God fret my fat, I don’t mean no offence.