You mean YOU were feeling weak and faint or do you mean the heartbeat was weak and faint?
Did you feel your pulse and time it? The reason I am asking is because my mom told me a story a few weeks ago, said she woke up with her heart pounding and pounding. Thought it would slow down, but didn't and she was getting all upset. Finally she said she took her pulse and it was going right in time with her sleep machine like it ALWAYS does (and that is 60 bpm!) it wasn't going fast at all! Maybe that happened to you too? Just anxiety making you think it was going fast. And if it was YOU feeling weak and faint you probably got yourself all upset over it.
And if it WAS going fast, you could have been dreaming something, a dream will do a number on your heart, emotions, etc.