Q: after downloading and opening Photos why is hard drive space doubled for pictures

It is not - it just looks like it is because of double counting  --  Photos saves disk space by sharing images with your iPhoto or Aperture libraries - Apple Support

LN

Yes - but the backup size is not related to your original question about hard disk space

Backups have no relation to your hard drive

LN

Because of the double counting Larry explained in an earlier post, the same set of pictures is counted twice.

I have no idea where you pulled that from, it is not what I said, I'm out now.

Good luck.

After installing Photos the drive now shows 200GB of data. I'm asking why would that be?

Probably when you upgraded to Yosemite TM sensed a complete change in system and backed up most of the drive again including the Photos library and counted that in it's size.  But that's not an issue with TM because as it needs more space it will delete the oldest backup to make room for the newest incremental backup.