Are there any lightweight flywheels for a 1996 1.5 BA? Had a look around online and didn't find anything really. Are there ones that would fit?

You can find some for 1.8 BP and you have to check if it's fitable on the 1.5.Sure the crank case are nearly the same, the 1.8 is beefier but they are looking the same.You will have to check wether the mounting holes are the same between 1.5 and 1.8 flywheels and if so maybe it could go with it.
Or you can do like i did, in my car tread somewhere i wrote when i made my overhaul on the Z5.
I have taken my flywheel to miling machine to remove/skimm maybe 1mm at the "glass" surface and to remove the balancing ring at the back.Sure i've removed arround half a kg(not much) but noticeable when driving.
it has to be balanced once again after the operation and after all math it's verry little gain so moust of the people would say it's not wort it.I could agree with them if i wasn't so into my F..
If you know what i mean..

Yea, I know what you mean. It's really not worth it then to be honest.