Great question! The VW 1600 cc engine was steel and weighs in around 250lbs. The 1800 cc suby engine is aluminium and weighs in at about 200lbs. So more power, less weight, all around better.
Actually, the VW Aircooled engine is mainly aluminum/magnesium alloy. However, fully assembled with cooling tin, carbs, flywheel, etc, it weighs about what you mention - between 200 and 250 lbs depending on options.
EA82 engine is 185 without flywheel, manifolds, and ancillaries (alternator, etc). So, fully assembled and dry, it should come out similar. But then you have the extra weight of the coolant - putting the rad up front helps for sure.