Unfortunately, weapon modifications do not address double weapons at all.
The available precedent—weapon special materials, magic weapon enhancement, and so on—treat the two ends of a double weapon as separate weapons.
you can build a double weapon with each head made of a different special material.
(Equipment → Special Materials)
Creating magic double-headed weapons is treated as creating two weapons when determining cost, time, and special abilities.
(Magic Item Creation → Creating Magic Weapons)
Weapon modifications should work the same way—but we don’t have any explicit rule saying that.
Anyway, treating the two heads as separate weapons can cause a whole lot of confusion—for example—but in this case, extrapolating this rule to weapon modifications actually works out pretty much the way you’d like it to. Since the two heads are treated as two weapons when determining special abilities, they can each be made dual-balanced and then you’ll be “wielding two weapons with the dual-balanced modification.”
Ultimately, RAW, you can argue that weapon modifications apply to the whole double weapon as just one weapon, but being inconsistent with literally everything else makes that a very poor ruling to make in practice.