I'm also overweight but do use a pair of lighter shoes for some fast sessions and short races.
I can summarise the results quite easily: yes, they do make me faster; yes they do cause problems with calf muscles, achilles, knees etc.
I think if you wear stable shoes the rest of the time you might improve times wearing lighter shoes for races. In fact the contrast seems to help. Why not try it on something like a 5k and see what happens?