Does a heavy darkwood shield count as a light weapon with regards to two weapon fighting?
No. Darkwood items do weight less then normal items, but weight has nothing at all to do with the effort needed to wield a weapon (light, 1-handed, 2-handed).
On a similar note, mithral weapons also do not change the effort needed to wield them. A Medium sized mithral longsword is still a one-handed weapon for Medium sized creatures.
Thanks!!