When targeting an enemy unit with either a phase weakness OR a weapon damage weakness, the in-game UI will describe the "Phase Weakness Effect" (+10% damage and +2 stability damage). This gives the false impression that phase weakness is the same as weapon damage weakness.
However, this is in fact not the case. Weapon damage weakness exists as a separate effect, and stacks with phase weakness. It is simply not shown properly in targeting preview. This is an important distinction since certain in-game mechanics interact only with phase weaknesses but not weapon damage weaknesses.
A recent example would be the final boss of Endless Projections, where certain effects are only triggered by phase weaknesses but not weapon damage weaknesses.