Excess fat, skin, muscle and even swelling can all contribute to lower lid bags. A detailed consultation will reveal which of these is contributing the most to your individual issue. There are excellent treatment options for each of these ranging from injections to laser to surgery.
To ensure you are receiving the highest level of care, seek out a modernly trained, new-school dermatologic surgeon, oculoplastic surgeon, facial plastic surgeon or plastic surgeon who is board certified and fellowship trained in one of these "core four" cosmetic specialties.
While I would need to see you in person to evaluate your situation, bags under the eyes are generally caused by pockets of fat. These can be moved into a better location during lower blepharoplasty. If there is excess skin present, that can be removed during the same procedure. The heaviness in your upper lids could be caused by a number of factors, but might be resolved by upper blepharoplasty, which would open the eyes. I hope this helps.
When performing a lower blepharoplasty procedure, the amount of fat and skin that is removed it is determined at rest, not upon animation. The fat is removed from the inside approach, also known as a trans-conjunctival approach. If there is excess skin present at rest, a small pinch technique is performed at the lash line. In our practice this incision was closed with tissue glue.
You need a personal consultation (or at least post a photograph) to address your concerns and determine what is needed to aesthetically help you. While some dermatologist do mid face treatment and even eyelid surgery, generally, I recommend seeing an aesthetically oriented oculoplastic surgeon for this assessment. Finding an individual like this may be challenging where you live.