The best way to dispose of your heavy mattress is to take it to a recycling center. Some facilities can pick them up from you and recycle them at a small charge.
If you cannot find a recycling center, you can break down the mattress and recycle the parts. You can also reuse the mattress parts for repair projects around the house or in making artwork and home decor.
You can also dispose of your old mattress at a waste disposal center that specializes in disposing of household items for a charge.