Welcome to Justanswer.com, my name is ***** ***** I will do my best to assist you.
You gave a ton of good information in your question, and that cuts down on my need to ask you a lot of questions in return.
The key piece of info is that you said t he charger light sometimes looks very weak. That tells us that your magsafe charger adapter is beginning to fail. It needs to be replaced.
Now depending on what exact model and version of macbook pro you have. You either need this power adapter http://amzn.to/1NOPwgj
Or this one. http://amzn.to/1JE7tZ4
Before ordering either though, reply and let me know the year and the size of your macbook pro, that way we can be certain were ordering the exact charger you need. Also, I would stay away from generics, the 20-40$ you save on a generic charger, isnt worth the damage it can do to your 1500$ + machine.
I strive to provide great service, and greatly appreciate a rating of excellent ( 5 stars ) selected and submitted below this answer or at the top right of the screen. I always answer follow up questions.
Senior Technician and Network Switching Systems Operator / Maintainer.