Droopy Eye Corner Skin After Blepharoplasty

There is a tradeoff on the medial eyelid skin. If the incision is too medial, it shows even when the eyes are open. A conservative approach is usually best so that the smallest, least visible correction can be made.

With lower eyelid surgery, it is vital that the surgeon does not remove too much skin, which can be very hard to correct. If there is some excess skin you can always go back and remove a little more easily. At only 5 weeks out, I would definitely wait because the skin may tighten on its own.
If nothing changes, and at 3 months your surgeon sees no swelling of the lower lid, then revision can be done at that time. Be sure to discuss your concerns with your surgeon so that they can be followed closely.
Dr. Miller

There are many patients who heal at different rates on both sides of the same surgery.  There are also preoperative asymmetries that can affect the ultimate result. 
Give this some time and see how things look at six months. If there is redundancy that concerns you, it is simple to correct.
 

Typically, I like to wait around 3-6 months prior to doing a revision because many times things will settle down with time. It is possible that if it is obvious on physical exam that I left a little too much skin I will do a revision sooner just so you can get on with enjoying your result.
Hope this helps.

The skin on the inside corner of the upper eyelid does take quite some time to settle down. There is occasionally some residual wrinkling that is present on the upper lid closest to the nose. The design of the upper lid crease and incision sometimes does not allow for full correction of all of the excess skin in that area of the upper eyelid. Sometimes a small tuck of excess skin can be removed, but careful attention to not make the incision more noticeable in that area is very important.