der Klotz
block
A large, solid, and often roughly worked piece of material, usually made of wood or stone.
Der Bildhauer begann seine Arbeit an einem großen Marmorklotz.
The sculptor began his work on a large block of marble.

block / oaf
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block
A large, solid, and often roughly worked piece of material, usually made of wood or stone.
Der Bildhauer begann seine Arbeit an einem großen Marmorklotz.
The sculptor began his work on a large block of marble.

The expression 'ein Klotz am Bein sein' (to be a burden/a millstone around someone's neck) is very common. The person burdened by something is in the dative. The expression describes a heavy burden or an obstacle.
Diese teure Wohnung ist mir mittlerweile ein Klotz am Bein.
This expensive apartment has become a burden to me by now.
When 'Klotz' (oaf) describes a person, it is colloquial and derogatory. It labels someone as coarse, clumsy, or slow.
Was stehst du da rum wie ein Klotz?
Why are you standing around there like an oaf?
In its literal meaning, 'Klotz' (block) is often combined with the material it is made of. Typical examples are 'Holzklotz' (block of wood), 'Steinklotz' (block of stone), or 'Marmorklotz' (block of marble).
Er spaltet den Holzklotz mit einem einzigen Axtschlag.
He splits the block of wood with a single axe blow.
burden / load
'die Last' and 'der Klotz' can both mean something that burdens someone. 'Last' is the normal word for a heavy responsibility, worry, or burden. In this meaning, 'Klotz' fits mainly in the fixed expression 'ein Klotz am Bein sein' (to be a burden / to be like a ball and chain). It sounds more figurative and often stronger: something or someone really prevents you from moving forward. The words can be confused because both can express a burden. But outside this expression, 'Klotz' is usually a large piece of wood or stone, not simply a worry.

Der alte Kredit ist für die Familie ein Klotz am Bein.
The old loan is a real burden for the family.
Nach dem Streit mit ihrer Schwester fühlt sich die Last für Maria noch größer an.
After the argument with her sister, the burden feels even greater for Maria.