For example, if I have a purple burning spellweave robe and upgrade it to gold, would there be any benefit to re-enchanting with a gold magic armor glyph?
The quality of the enchantment improves automatically on upgraded dropped gear ... provided that you haven't already re-enchanted the gear in the past.
In other words, (a) any crafted gear or (b) any dropped gear where you've applied a new enchant will require a new enchantment upon upgrade.
The simplest way to see whether a piece needs a new enchantment is to view the gear piece in the upgrade section of the crafting table ... before you actually upgrade it. In the OP's example, take the Burning Spellweave Robe to any clothier table and view the gold-upgraded robe in the UI before actually applying the dreugh wax. The UI will tell you if there is any improvement on the enchantment.
Straightforward, I think, but I can post some screenshots if a visual would help.
I'm pretty sure that enchants don't upgrade with gear, the multiplier in which said enchant is affected by does giving the impression of upgrade but it would still be beneficial to get a gold glyph for maximum effectiveness. Could be wrong though...
Rhaegar Gregorson, The Ebonheart Centurion - Imperial Dragonknight RABIDxWOLVERINE - Xbox One, NA, Ebonheart Pact