Still Swollen 4-Weeks Post Eyelid Surgery, Are There Malar Bags?

Malar swelling 4 weeks after routine lower eyelid surgery is a bit unusual.  However, sometimes surgeons add a bit of a midface lift with the lower eyelid surgery and this could account for a more persistent swelling.  At this point, your only real option to to allow the lower eyelid to heal.  It is improbable that actual swelling will persist more than 4 months (a lifetime).  Midface irregularities including a festoon that did not exist prior to surgery is often best addressed with a bit of Restylane filler.

You are likely referring to malar bags or "festoons".  This is the area of the face that acts as a sponge.  They should improve with time since it has been only one month from surgery.  Ask your surgeon.

The swelling resting on the cheeks after lower lid blepharoplasty are probably malar bags.  In my experience, there is usually some evidence of malar bags before surgery (look at your pre operative photos) and the resultant inflammatory fluid from surgery settles in these unnoticed bags, making them prominent.  It may take up to three months for the swelling to dissipate. Hang in there! 

Malar bags are retained fluid from chronic tissue swelling and would not be caused by a lower eyelid surgery however, if you had significant lower eyelid fat bags as well as malar bags, the malar bags may become more apparent after the fat bags are removed.  You should have this discussion with the surgeon that did your eyelid surgery.