
stemmen
to lift
To lift or press up something heavy with great physical effort.
Der Gewichtheber konnte die Hantel mühelos über seinen Kopf stemmen.
The weightlifter was able to lift the barbell over his head effortlessly.
to lift / brace / manage
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to lift
To lift or press up something heavy with great physical effort.
Der Gewichtheber konnte die Hantel mühelos über seinen Kopf stemmen.
The weightlifter was able to lift the barbell over his head effortlessly.

to brace oneself against
To press against something with force in order to resist it. Also used figuratively for opposing a development or decision.
Die Anwohner stemmten sich erfolgreich gegen den Bau der lauten Fabrik.
The residents successfully braced themselves against the construction of the noisy factory.

to manage
Informal for handling a large, difficult task or challenge.
Ich weiß nicht, wie wir dieses riesige Projekt finanziell stemmen sollen.
I don't know how we are supposed to manage this huge project financially.

to chisel
In crafts: to make recesses or holes in wood or stone with a chisel.
Der Zimmermann musste eine Nut in den Holzbalken stemmen.
The carpenter had to chisel a groove into the wooden beam.
The different meanings of 'stemmen' share one idea: you apply great force or effort to overcome resistance. That can be a heavy weight, a problem, or a difficult task.
Sie musste den schweren Koffer auf das Gepäckband stemmen.
She had to lift the heavy suitcase onto the luggage belt.
In the literal meaning, 'stemmen' is always used with heavy objects. Typical objects are 'Gewichte' (weights), 'Hanteln' (dumbbells/barbells), 'Möbel' (furniture), or 'Kisten' (boxes/crates).
Zusammen haben wir das Sofa in den dritten Stock gestemmt.
Together we lifted the sofa up to the third floor.
In the meaning 'Widerstand leisten' (to resist), the verb is reflexive and is always used with the preposition 'gegen' + accusative: 'sich gegen etwas stemmen' (to brace oneself against something / to resist something).
Die Mitarbeiter stemmten sich gegen die geplanten Kürzungen.
The employees braced themselves against the planned cuts.
The meaning 'eine schwierige Aufgabe bewältigen' (to manage a difficult task) is informal. It is often used for major challenges, especially financial or organizational ones.
Als kleines Unternehmen können wir so einen großen Auftrag nicht allein stemmen.
As a small company, we can't manage such a large order on our own.
This meaning of 'stemmen' is a technical term from crafts, especially woodworking and stoneworking. You can recognize it from the context and often from the mention of the tool, the 'Stemmeisen' (chisel).
Der Tischler stemmte ein Loch für die Verbindung in das Holz.
The cabinetmaker chiseled a hole in the wood for the joint.
to lift
Heben and stemmen can both mean moving something upward. Stemmen emphasizes the great physical effort and resistance involved, while heben is more general. Use heben for the ordinary process and stemmen when the weight is particularly heavy.

Wir mussten die schwere Kiste mit großer Kraft stemmen.
We had to heave the heavy crate with great effort.
Wir müssen die Kiste gemeinsam heben, damit sie nicht fällt.
We need to lift the crate together so it does not fall.