An Etymological Dictionary of the German Language/Annotated/Steuer
Steuer (1.), feminine, ‘aid, tax, duty, impost,’ from Middle High German stiure, Old High German stiura, feminine, ‘duty, tax,’ properly ‘aid, contribution, support, help.’ With these general meanings the following word is connected.
Steuer (2.), neuter, ‘rudder, helm,’ from the equivalent late Middle High German (Middle German) stiure, neuter; properly a Low German word, originally belonging only to the Teutons on the sea-coast (in Old High German stiura, feminine, ‘rudder, stern'); compare stuur, ‘rudder,’ Anglo-Saxon steór, neuter (English stern, see under Stern), Old Icelandic stýre, neuter, ‘helm.’ To this is allied steuern, ‘to steer, pilot,’ which originated under the influence of the substantive Steuer, from Middle High German and Old High German stiuren, ‘to guide, lead, support'; compare Dutch stieren, sturen, Anglo-Saxon stŷran, English to steer, and the equivalent Old Icelandic stýra (Gothic stiurjan), ‘to fix firmly, maintain.’ These cognates, on account of their undoubted connection with Steuer, feminine, ‘duty' (literally ‘support’?), have been linked with Old Icelandic starr, ‘stake,’ and the equivalent Greek σταυρός.