it may mean that u have asthma.. i would suggest that u go and see the doctor
When does that feeling of 'heaviness' happen? Do you feel that after doing a strenuous activity? Or do you feel that in certains positions such as lying on your back? Do you have difficulty in breathing? That symptom can mean something and you should go and see your doctor. Take care.
Where at in your chest. does it radiate anywhere . Do u get nausea or have a cardiac history. Hows your bp. Need more info than just heavyness n chest.