Hi all,
Well I have a 7 string Streamer and it feels weighty, but I didn't notice any problem with neck dive, the thumb could be a very different beast.
I got used to the weight and the playing gets a bit different, but it is doable. I had to readapt when I had to go back to lighter instruments due to back injury.
Now I have noticed that the thread is quite old, so this will probably be of little help, but if you want to know anything in particular about 7 string Warwicks, just PM me or reply to this thread.