Do you lose more weight jogging with a bin bag under your shirt?

Answer 1

Kinda-sorta.

The bin bag will make you sweat more, so you'll lose more weight by losing more fluid(=water) from your body.

Trouble is, once done with your run you'll get thirsty. And when you drink you'll put that extra weight lost by the bin bag right back on.

Answer 2

You'll sweat more.

And temporarily lose a bit more weight (that's water weight - not fat. You can't sweat out fat, no matter what the Shopping Channel is trying to tell you) through the sweat dripping off your body.

Then you get thirsty, drink, and put the extra weight lost right back on.