I think most of the weight was being held by the fillet for most of the day, and it wasn't uncomfortable. I had an auxiliary strap which was supposed to pass from the nape of my neck over the temples and then up the crown, to secure the veil in the center and help support the weight. That didn't work so well. As has been my experience with modern elastic circular headbands meant to be worn the same way, the thing slipped off the back of my head repeatedly. Didn't matter if I fastened it over or under my hair. I wasn't careful about pinning it to the fillet at the temples; maybe that's the trick.
The obvious options are 1) try again with better pinning, 2) do away with it or 3) use a chin-strap/wimple instead. I'm not sure when the wimple starts showing up, but I believe Walton Rogers shows it in her book (which covers the era up to 700 CE) as a possibility. I believe I will try options 1 and 2 first, as I am not a big fan of things on my neck, particularly in the heat.
Upon an amblere esily she sat,
Ywympled wel, and on hir heed an hat
As brood as is a bokeler or a targe.
- Chaucer describes the Wife of Bath on her horse, wearing a wimple and a hat as big as a small shield