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Old English weldan (Mercian), wieldan, wealdan (West Saxon) "to govern, possess, have control over" (class VII strong verb; past tense weold, past participle gewealden), merged with weak verb wyldan, both from Proto-Germanic *wal-t- (cf. Old Saxon and Gothic waldan, Old Frisian walda "to govern, rule," Old Norse valda "to rule, wield, to cause," Old High German waltan, German walten "to rule, govern").
The Germanic words probably are from PIE *waldh- (cf. Old Church Slavonic vlado "to rule," vlasti "power;" Lithuanian veldu "to rule, possess"), from root *wal- "to be strong, to rule" (see valiant).