I think you're looking at it wrong.
The 159 isn't a heavy car, not really.
if you compare something like the 159 2.4 vs the BMW 325d there is only about 50kg difference in the weight. An Audi A4 2.7 of comparable age comes in around 10kg heavier and with less power than the 159, so it is actually about right when compared to some of the more mainstream competitors.
Where as the 156 with the same 2.4 motor is a good 200kg lighter. Not because the 159 is a much much fatter beast but because they worked very hard on the 156 to keep the weight down using expensive metals, process techniques etc.
You're better comparing the 166 to the 159 though as they're more closely related in every way other than name and the weights come in around the same with those as well.
1999 156 1.8TS Sport Pack 3
2001 166 3.0 V6 24V Super
2003 156 GTA 3.2 V6 24V
2005 156 1.9 JTDM-Jet Sport
2008 159 1.9 JTDM Lusso
1997 GTV 2.0TS Lusso
2001 147 1.6TS Lusso