When a fuse blows it is best to replace it with a bigger fuse so it won't blow the next time?

Absolutely not. A fuse is a safety device designed to fail when a large current is passed through it. By blowing it protects delicate components in the rest of the circuit. The fuse is there to protect the wiring within the circuit from overheating and catching on fire. It is not there to protect anything plugged into that circuit. Use a larger fuse and you may cause a fire.