Ich stütze mich auf den Tisch, weil ich müde bin.

Because sich stützen is commonly used as a reflexive verb when someone supports or braces themselves.

So:

• Ich stütze mich = I support/brace myself
• Du stützt dich = you support/brace yourself
• Er stützt sich = he supports/braces himself

Without the reflexive pronoun, the meaning changes:

• Ich stütze den Tisch would mean I support the table.

So mich shows that the action comes back to the subject: I am supporting myself.

Here, stützen means something like:

• to support oneself
• to brace oneself
• to lean on something for support

In this sentence, it suggests that the speaker is tired and is using the table to help hold themselves up.

It is a bit more specific than just lean. Sich auf etwas stützen often suggests using your hands, arms, or body to take some weight.

Because auf is a two-way preposition. It can take:

• accusative when there is movement toward something or contact being made
• dative when something is simply located somewhere

In Ich stütze mich auf den Tisch, German treats this as directing your support onto the table, so it uses the accusative: den Tisch.

Compare:

• Das Buch liegt auf dem Tisch. = The book is lying on the table.
  (location, so dative)

With sich auf etwas stützen, the normal pattern is auf + accusative.

Because Tisch is a masculine noun:

• nominative: der Tisch
• accusative: den Tisch

Since auf here takes the accusative, der changes to den.

So:

• auf den Tisch = onto/on the table, with accusative

Because weil introduces a subordinate clause, and in standard German, the conjugated verb goes to the end of a subordinate clause.

So:

• main clause: Ich stütze mich auf den Tisch
• subordinate clause: weil ich müde bin

That is why it is weil ich müde bin, not weil ich bin müde in standard German.

In German, subordinate clauses are normally separated from the main clause by a comma.

So the comma in:

• Ich stütze mich auf den Tisch, weil ich müde bin.

is required because weil ich müde bin is a subordinate clause.

Sometimes, but the meaning is slightly different.

• sich auf den Tisch stützen = to support/brace oneself on the table
• sich an den Tisch lehnen = to lean against the table

So stützen focuses more on using the table for support, while lehnen focuses more on leaning your body against something.

They are related, but not always interchangeable.

Because the second part is a full clause with its own subject and verb.

• Ich stütze mich auf den Tisch = main clause
• weil ich müde bin = subordinate clause

Just like in English, you repeat the subject:

• I lean on the table because I am tired.

German does the same thing here.

Yes. You can say:

• Weil ich müde bin, stütze ich mich auf den Tisch.

That means the same thing.

Notice what happens in the main clause after the subordinate clause:

• stütze comes before ich

This is because the subordinate clause takes the first position, so the verb of the main clause must still come in second position.

Because in German, all nouns are capitalized.

So:

• der Tisch
• das Buch
• die Müdigkeit

That is why it is Tisch, not tisch.

Also, Ich is capitalized here because it is the first word of the sentence. Unlike English, German ich is not normally capitalized in the middle of a sentence.