2.) As it was hot, he was only wearing a pair of shorts.

3.) Since he was on a diet, he could not eat the pudding.

In each of these three sentences, the words “because,” “as,” and “since” all mean the same thing, and are interchangable.

The rule that I see is that when these words are used to describe WHY something is happening, they are interchangeable.

As James and Kate are friends, they went to the party together.

Since James and Kate are friends, they went to the party together.

Because James and Kate are friends, they went to the party together.

However, the use of ‘as’ and ‘because’ in this context are discouraged because (as, since) they are prepositions and prepositions are not supposed to be used to begin and end a sentence.

‘As’, ‘Since’, and ‘Because’ can also be used in different context where they don’t mean the same thing.

As sure as the sun rises everyday, I’ll be there. (‘As’ is not interchangeable with ‘since’ and ‘because’. The sentence will have a different meaning.)

Since the middle of the 15th century, Ireland has become a part of the United Kingdom. (Again, ‘as’ and ‘because’ will give a different meaning.)

The American Civil War was fought because the emancipation law was passed. (‘Because’ here is causal.)

because

The reason is very important in the sentence, so because comes in the sencond clause of the sentence.

Example: I read this book because I like it.

as

The reason is already known.

Example: As we read, we learn.

since

The reason is already known.

Example:

(more formal than as) Since we were in the computer lab, our English has improved.

for

The reason is given at the end of the sentence.

Example;

We went to a small restaurant – for we were hungry.

Good Luck!

http://www.englisch-hilfen.de/en/words/because_as_since_for.htm