The roots will not be affected by the weight of the orchid, it's when you squeeze them in that some might snap.
Unfortunately the rim of your vase is not ideal for what I do which is take a couple of plant sticks and poke them through the holes of the net pot - like this the net pot rests on the rim of the pot taking all the weight with the roots dangling below.
Maybe you can still glue a thin piece of wood across the rim which the net pot could then rest on taking some of the weight off.
Otherwise bigger vase which starts to become expensive so if mine ever get that big I have already decided to use plastic rubbish bins (10l) as pots if it ever gets to that stage. Won't look as good but the Ikea bins are pretty stylish, I have used one as a lamp shade before