You were exhausted because you walked all the way home.
but is the best choice
The correct way it should be stated would be = He was exhausted, yet he*** walked all the way home. = ***the second he may be omitted
Any of the conjunctions could be grammatically correct, depending on what you're trying to say. If your meaning is "Even though he was exhausted, he walked all the way home," or, despite how tired he was, he still walked home, "but" is the appropriate conjunction. He was exhausted, but he walked all the way home. If you instead mean that the cause of his exhaustion was his walk home, "because" should be used. He was exhausted because he walked all the way home. "And" is probably the weakest choice of the three, but is still grammatically correct. It conveys a similar meaning to the sentence using "but." He was exhausted, and he walked all the way home.
In conjunction with
The correct spelling is exhausted (worn out, or used up).
The correct spelling of the conjunction is because (due to, owing to).
That is the correct spelling of "exhausted" (fatigued).
The likely word is the conjunction or preposition because(indicating a cause and effect).
And is a coordinating conjunction; therefore it should never begin a sentence. Ironically, though, the preceding sentence is correct because and is used as a word, not as a conjunction.
exhausted
Yes, this is a fused sentence because it combines two independent clauses without proper punctuation or a conjunction to separate them. To correct it, you can add a semicolon or a conjunction like "but" or "and" between the clauses.
That is the correct spelling of "bleary" (blurred, vague; or exhausted).