Best Laser Treatment for Under Eye Bags?

The short answer is yes, laser can be highly rejuvenative to lower lids if skin changes are a main factor. Bags under the lower eyelids are usually caused by displaced fat, redundant muscle, redundant skin, or sometimes even a prominent vascular plexus giving the aesthetics of lower lid bags or dark circles.
Early volume loss in your upper cheek and tear trough area can exacerbate even a small amount of genetic predisposition to having eye bags. There are numerous, good options to address this issue ranging from nonsurgical to surgical. Which treatment option is best will depend on the underlying cause of the bags
It is important to realize that it is displacement of fat, NOT just excess fat that can cause lower lid bags. Old school blepharoplasty approach took skin and fat out of the lower lids by cutting right through the skin, which gave long term poor results with hollowed out lower lids and more potential for surgical complications. 
We know that we tend to lose fat as we age in our face, so taking more out as part of a surgical procedure may look good immediately, but it is a long term bad idea. Newer surgical approaches to lower lid blepharoplasty do not cut through the skin and leave no external scars, this is called the transconjunctival approach. More important yet, the existing fat is repositioned instead of removed, giving much better long term results with a more conservative surgical technique that also has lower potential for complications. 
Nonsurgical options include strategically placed volume to replace early loss, which can have a dramatic impact on the appearance of eye bags and the junction between your eyelids and cheek. Volume can come in the form of fillers or as micro fat grafting. 
Laser resurfacing can also address these areas when skin changes are the prominent player. 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. Membership in organizations like the American Academy of Facial Plastic and Reconstructive Surgery help to identify a highly trained surgeon. Cameron Chesnut #realself500 Physician 

Treatment for under eye bags vary depending on the severity of the bags. Also, some people confuse under eye bags for hollows under eyes, so the treatments vary. Without a picture it is difficult to say which would be ideal for you. Laser treatments are generally great for under eye skin that is becoming 'creapy' and 'wrinkly'. The laser causes damage to the skin which in turn stimulates it to repair itself and while doing so, activates skin cells to produce more collagen and makes it appear more youthful and tighter. (see my before and after gallery- there is a picture of fat transfer with under eye laser)Other options include fillers and surgical options. 

Thank you for your question. There are many things you can do to treat under eye bags, but a combination approach with nonsurgical treatments would give the most improvement: fillers (Belotero, Juvederm Volbella), lasers (Fraxel/CO2), Renuvion (J-Plasma), microneedling/PRP, Cosmelan peels and stem cells. A surgical option to remove skin and/or fat might be the best solution long-term. I suggest getting a formal evaluation with a cosmetic dermatologist to see what is best for you and your goals. Best, Dr. Emer.

Lasers (and chemical peels) can tighten the crepe lower lid skin and reduce the appearance of mild lower lid bags. However, large bags are due to  herniated fat pads and usually require removal and possibly skin tightening, as well. See a surgeon who provides all these treatments to get the best advice on how your should proceed..

It is hard to answer this question without a picture.  You simply may need a small amount of filler to improve your bags.... There are a wide range of causes for lower lid bags and each should be approached differently.  Please find an experienced surgeon to help you make the right decision.
DR Z