Do I apply Weakness for Moltres' "Inferno Wings" attack if I do the extra 70 damage?
Inferno Wings will not apply Weakness, regardless of whether you do the extra 70 damage or not.
Source: Brilliant Stars FAQ; TPCi Rules Team (2022-02-24)

Relevant cards

Note: All applicable cards may not be listed below.
SWSH9_21
SWSH9_21