Why my car has a week start?

Since no one answered yet, and I don't know how much experience you have with vehicles, but I would go to the basics. Your car is now 12 years old, battery, and or connection to the battery are a good chance of causing the problem. Check for a clean tight connection at the battery cables. Charge your battery and see if that makes the difference. If the lights brighten when you accelerate, it could also indicate an alternator problem that is not charging your battery well enough.