Perhaps a distinction more functionally significant between aspis and thureos than weight would be the way each shield was held?

IIRC, the thureos had a single central hand-grip, while the aspis used the hand and forearm system. I would guess this difference should have an effect on how much protection each fighter can expect from its own and its neighbor's shield and, hence, on the general fighting style and details such as the way weapons were handled etc...

Cheers
A.