It is not uncommon to experience different sensations and symptoms during each pregnancy, even if you have had previous pregnancies. Feeling a sense of heaviness or pressure on one side of the abdomen can be attributed to various factors such as ligament stretching, hormonal changes, or even the position of your baby. As long as you are not experiencing severe pain or bleeding, it is likely nothing to be concerned about. However, it's always best to consult with your healthcare provider who can provide a more accurate assessment based on your individual circumstances. They may recommend an ultrasound or further tests to ensure everything is progressing normally with your pregnancy.