Technically speaking, an EV will be lighter when the batteries are discharged. Not that anyone is going to notice or appreciate the difference.

Note: This has no impact on your argument. I only mention it because I love me some physics.

Here's a citation, if you're curious:

https://physics.stackexchange.com/questions/34421/does-the-m...

The short version is that it will have less mass when the battery is discharged. However, you're not going to be able to detect a difference on your bathroom scale.

Again, this is being posted as a mere factoid and not meant to argue your point.