to prove / show
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to prove to be
To turn out to be something specific after closer examination or over the course of time; to prove to be true or false.
Die anfängliche Vermutung erwies sich bei näherer Untersuchung als korrekt.
The initial assumption proved to be correct upon closer investigation.
The prefix 'er-' is inseparable. It remains firmly attached to the verb stem 'weisen' in all tenses and sentence positions. The past participle is 'erwiesen' (proven).
Die Theorie wurde wissenschaftlich erwiesen.
The theory was scientifically proven.
The two meanings have very different sentence structures. The reflexive form 'sich erweisen als ...' means 'to turn out / prove to be'. The structure 'jemandem etwas erweisen' means to show someone an honor or do someone a service.
Das Gerücht hat sich als wahr erwiesen.
The rumor proved to be true.
This meaning is almost always used in the fixed structure 'sich als ...' + adjective or noun in the nominative. It describes a result or realization.
Die Aufgabe erwies sich als schwieriger als gedacht.
The task proved to be more difficult than expected.
The meaning 'jemandem eine Ehre/einen Dienst leisten' (to show someone an honor / do someone a service) is formal and used in elevated language. It always requires a person in the dative and a thing in the accusative.
Ich möchte Ihnen meinen Respekt erweisen.
I would like to show you my respect.
to perform / afford
'leisten' and 'erweisen' can both be used when someone gives or shows something to another person, for example help, a service, or respect. 'Leisten' is more neutral and works well with concrete help, work, a service, or resistance. 'Erweisen' sounds more formal or elevated and often appears with words like 'Ehre' (honor), 'Respekt' (respect), or 'Dienst' (service). Learners may confuse them because some fixed expressions express similar things. But usually 'Hilfe leisten' (to provide help) and 'jemandem Respekt erweisen' (to show someone respect) sound natural.
Die Kollegen erweisen dem alten Chef bei der Feier großen Respekt.
The colleagues show the old boss great respect at the celebration.
Du leistest deiner Freundin große Hilfe beim Umzug.
You are a great help to your friend with the move.