Outlet Melting?

I'm not an expert, but what is happening is not good! There may be a problem with the grill itself, such as drawing too much electricity, or the outlet might be old or damaged. The outlet also might be on a circuit that already has too much plugged into it. You have to watch the wattage of your appliances and other items, and stay under the load limits of your circuit. Most houses seem to have 15-amp circuits, which means you should stay under 1500 watts total on that circuit. There should be a circuit breaker that trips and cuts the power when there's too much draw on the circuit, and if this hasn't happened, there's something wrong.

In addition, your kitchen and bathroom outlets should be GFCI outlets (Ground Fault Circuit Interrupters), which have their own, built-in circuit breakers. These can prevent shorts and electrocutions because you're always around water in bathrooms and kitchens.

You should really have a professional electrician check your outlet and your circuits, because you are in danger of having a fire. Also have someone test the grill, but I don't think you should use it until you get the other things checked. Don't take chances! The life you save may be your own.