According to the wiki, weakness to fire will not boost the damage from fire spells when the effects are in the same spell. I believe this also means even if duration is added to the spells. So the recommendation for maximum damage would be two spells, one that weakens to fire (and possibly weakness to magic as well which will boost the fire spell's damage multiplied by the fire weakness) and then a spell to do the damage.
Depending on your Magika, or how often you want to be able to cast this spell combo, you could set the duration of the weakness to a short amount, long enough to switch spells and cast the actual damage spell, or perhaps increase duration and make it so you can also increase the duration of the damage spell. For the latter, you'll have to determine how long in seconds it takes you personally to switch spells and cast in order to optimize the ratio of damage to duration.