And obviously the subject will also be subject to said damage.
What if it fails to penetrate their Magic Resistance? Does it fail to generate and 'stick' to them, or does it just fail to harm them while they run around on fire?
If a spell fails to penetrate magic resistance, the spell fails entirely on the resisting target; in this case, the target is not 'coated' in flames.
A group level version of this spell cast on a party of, say, a mage and a few grogs would result in a resisting mage not being coated, but the grogs would be, presuming they have no magic resistance of their own and are not under the mage's Parma.
HoH:S provides us the standard that it's PeTe magic to make armor weightless, but still generates a Load due to bulk. Is it safe to presume that PeTe(He) (Base 5) is the standard to make a wood staff weightless and an actual Load of 0? Could you get away with it by using MuTe(He) Base 3, or even just MuHe Base 3?
How would making a weapon weightless affect its combat statistics in the AM paradigm? Depending on the answer, making a weapon weightless might actually be a bad idea; Hacking someone with a foil vs. hacking them with zweihander yields much different results.
Rego might be better, if you can create a suitable/workable variant of the Unseen Arm that "carries" the weapon's Load?
Regardless of how one might make a weapon weightless it becomes problematic for beings with magic resistance. It becomes a device with an active effect and the RAW would seem to hold that if the effect doesn't penetrate MR then the weapon would be resisted, too. It's a common house rule, though to ignore magical effects and apply weapon damage if an effect would be resisted.