You are long past dead when the weight becomes an issue.
At least in a little plane. The shape of the ice buildup can
be really ugly.

Worse problems: Shape of the wing drag
Tail plane stalling in landing
configuration.

Airplanes with the spar in the front seat tend to carry ice
better-- the ugly shape interferes less with the wing lift.

Trust me on this. Bill Hale BPPP instructor

gwengler wrote:
Just that the change in shape of the airfoil is probably more important
than the weight.

That is correct, but at some time, the weight itself becomes an issue,
too. I was just curious about the weight. There are some interesting
pictures here comparing a Cessna wing with a TKS equipped Cirrus wing:
http://www.ferryflights.org/Ferryflights-icing.htm

Gerd