I would like to know how Germans differentiate between wägen and wiegen. When it comes to past participle both changes to gewogen (of course, the simple past is also wog)
Do Germans just know them by context?
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It is not entirely uncommon to inflect wägen like a regular verb (Duden), i.e.:
wägen, wägte, gewägt
This allows for a differentiation to both verbs wiegen, which can only be inflected as follows:
in the sense of to weigh: wiegen, wog, gewogen, wöge
in the sense of to sway or to rock: wiegen, wiegte, gewiegt