More layers of a lighter fabric will always be stiffer, due to the relationship of the fibres within the laminate, in the same way that a cored sandwich panel works. A single layer of 650g is able to stretch as much as the fibre will allow because there is nothing preventing it from doing so, it is only the single fibres in each direction that experience tensile and compression forces.
3 layers of 200g, whilst being the same thickness as the 650g, will be stiffer because it has a top layer and a bottom layer that must move relative to each other and a neutral layer in the middle that holds them together and doesn't allow that relative movement.
Then you have other factors like the fact lighter weight 200g fibres are smaller and so have less 'kink' at the weave intersections where the fibres pass over and under each other, meaning the fibres are flatter and more in line. A 650g being a thicker fibre has more kink, and hence is not as flat. Under tensile load, these kinks in the fibre try to straighten out and allow movement in the fibres.
Composite reinforcements work much better in layers. The heavier weight fabrics are intended to bulk out laminates where you would otherwise have to do many layers, using more material and taking more time. For the most part, they are only really beneficial from a cost perspective.