Alan, I apparantly did not respond to your post concerning the curious appendage at the back of the helmet, and quite honestly that fixture has continued to perplex me ever since. Actually I did not mean of course that this was a belt hook
but it reminded me of one in its appearance. You are quite right, jousting armor was quite heavy, and it seems apparant that the helm at Henry V's tomb at Westminster is an item of this type.
I have discovered more on the funerary achievements at Henry's tomb, and it does seem that some of the items were 'disturbed' during the Reformation, and there are certain reservations whether the helm and the sword are actually his or perhaps replacements. One reference even claimed there was a dent in the helm received at Agincourt, which seems odd as this was a jousting helm, not a combat one.
Another reference noted that at some point after the helm was placed at the tomb originally it was in some disrepair and damage at the peak of it was repaired and crest removed. It is noted in this discussion that at this point the helm was rehung with the iron hook affixed at the back.
This would suggest that these 'hooks' were probably fixtures attached to helms which had become funerary achievements in churches tombs, much as the case with Henry V's helm.
In an article in "The Connoisseur" (1902, Vo. 3. p.38, unnamed author) it notes that armour found in churches has often been tinkered with and adapted to funeral purposes even when not necessarily belonging to panoply of the interred.
I am inclined to think that perhaps this helm shown by Jean-Marc may be an authentic combat helm which later became a funerary achievement, suggested by the hook at back. It seems that affixing the helm in normal cases to the rest of the harness was through attached loops at front and back at base, or often by the T or cross apertures at the face which received a toggled chain.
Just wanted to add this additional info which I have found over the past week in various entries. Also, armor in these times was actually not bright but the metal treated in various ways, sometimes even painted, to prevent or at least dissuade rust. One method was fire bluing, but also used was 'russeting' or browning which promoted uniform but controlled rusting which could be checked.