Why does my Central A/C Keeps Blowing its Fuse?
Long-term darkening of a fuse on a high-draw circuit like an AC is not unusual. However, darkening as quickly as you have described means the fuse is operating right at its limit for too long.

The first thing I would do is call an electrician and have the fuse replaced with a breaker. At least that way you don't have to touch a hot fuse to replace it. They may also find a problem with the wiring (corrosion or a break) that could explain your problem.

Next is I would buy/borrow a multimeter that has an amp clamp on it. Measure the current used by various parts of your system (blower motor, compressor, condenser fan) as well as the main power feed to find out how much current you are pulling. This may help you identify which component is causing the problem.