King Reza: I may be wrong, but I think that there is no difference between those sentences in terms of their meaning and effect. However, “by” implies some tiresome activity having been performed for some time before the end of the day and emphasizes the end of the day as the time when we were all tired as the result. On the contrary, the sentence with “at” merely states that we were all tired and when we were all tired, irrespective of what caused our tiredness and in particular when the cause of our tiredness occurred. (It was extremely hard to convince the Greenpeace people that the global warming is a hoax and we were all tired by the end of the day. vs We were all tired at the end of the day and none of us wanted to go to the movie theater.)

But I would definitely wait for a native speaker to comment on this. Who am I to interpret the English language? :)

Pedro Martínez:

Pedro Martínez: Thanks a lot. You're really helpful.