The heaviest bass I've played was a MK Deluxe 5 with a Balance K body-coco bolo/mahogany-which probably weighed in at 13-14 pounds. 81-1952 (John's Series I) is the runner-up in this category.
 
The heaviest instrument I've ever played was a sousaphone, weighing in at 25-30lbs.

Rami, that's pretty darned heavy! I must admit that although I know loads of players who prefer heavy instruments for tone and sustain, the majority of instruments that I've loved most in terms of tone have been very light; the whole insrument has been very resonant. All the best Fenders I've played have been relatively ight, same with Rics (my 72 is around 8 pounds and is my favourite sounding Ric ever by far), same with Wals, Jaydees, pretty much everything. Everyone is bound to have different prefences though.  
Can't speak for Alembics because apart from an Essence I once played the only Alembics I've played which have been relatively light have been the set necks, and of course they sound different anyway.

Heaviest bass I've played is Mike Pisanek's 6 string Europa. feels like it's at least twice as heavy as my rogue 5.
 
Graeme

My 1993 MK standard, I am sure the previous owner didn't want the hollows in the body and went for the full solid body..
My 83 Squier feels like it is made form balsa compared to that!!

I think the hollow wings on the Signatures is a relatively recent thing Terry.....all the Signatures I played before mine had solid bodies and weighed a ton.

bigbadbill..I thought they all were hollow inside on the upper bout..I am used to it but sometimes it seems to love gravity and pull my shoulder off!
We could always go for posh plastic..graphite but there would be no nice wood grain to look at.

Wow look at the pretty striations in that pvc!
 
... Nah, just not the same thing
 
Mike