Puffy and Hyperpigmented Under Eye Area After Pearl Fat Grafting

Fat grafting by any technique is a tricky process for the lower eyelids. Grafts take a long time to incorporate, metabolize and stabilize. most surgeons perfoming a great number of lower eyelid revisional cases wait six months before assessing the final results. However that does not mean you should not be seeing your doctor for microadjustments during that period; this is important as well.
With a negative vector face, prominent eyeballs and flat cheeks, the problem with the lower eyelid is especially difficult. Some surgeons recommend soft tissue augmentation of the cheek area, in our practice with LiveFill, along with a superficial cheeklift to reduce, but not eliminate the problem.

There is no easy answer here.
It is possible that your fat grafts will persist and remain firm.
However, it appears that your cheeks and body rim remain untreated with relative lack of projection as discussed by Dr. Moelleken and termed the "negative vector" look.
For the most immediated option, I would advise fillers to the tear trough, infra- orbital rim, and malar eminence as experienced by Lucetted in the comments section. I would advise the use of Juvederm, but an experienced injector can do well with nearly any filler.

Unfortuneately, you have a common stigmata after standard blepharoplasty, which is hollowing under the eye. 6 weeks post-procedure is still very early and you will need to wait months to know what your results will look like. Generally speaking 20-30% of fat will survive, but sometimes none of it does. Every patient is different. Often times injecting any type of fillers into this area will cause the pigment under your eyes to become more noticeable because the skin is very thin. Fortuneately this hyperpigmentation is almost always temporary. I would talk to your surgeon periodically. Massage may also help reduce swelling and speed up your recovery time. Good luck.

It is generally believed that after fat transfer you won't get a sense of what fat will have survived the procedure until the 6 month mark. At that point, if more needs to be placed, or some needs to be diminished, appropriate steps can be performed.
Just by your pics it's hard to know if removing fat or adding more to the area below the puffiness would be appropriate. So unfortunately, waiting is your best option.