My thoughts, for what they're worth.
The vase is NOT Nazeing. You describe it well and the photos, especially the base, both help. You have noted the weight, which as you say is heavy for general Nazeing wares. The colour is too muddy, or dull, for Nazeing, and the pontil is a good symmetrical round shape and brightly polished. Three characterisics that say it is not Nazeing. This, and some of the other items that I have seen with the same green colour, thickness of glass and finish are known Stevens & Williams shapes - so that is a possibility for the vase.
Personally, I find the green a little too garish and bright for Nazeing, but other characteristics, such as the thickness of the glass and the shape certainly suggest that factory.