Tightening skin beneath eyes
Eyelid skin can be addressed surgically with a blepharoplasty, but this will not change the skin quality. Resurfacing with fractionated CO2 can be quite helpful. I have seen the most dramatic improvements with sublative radio frequency treatment. This improves fine lines and stimulate collagen to tighten the existing skin. This ultimately produces an extremely natural look.
IF you have just excess skin this can be removed surgically.
However, you will never get the super smooth look you see in the mirror when you just pull on the skin. As skin ages, the texture will change due to decreases in elastic tissue and collagen. When skin is excised, there will be less bunching of the skin, but the skin itself will still be of poor quality. Laser resurfacing can help with this as it should stimulate new collagen production in the skin. Fillers will also help as they provide support to the skin and "stretch" it out. You need a consultation with a cosmetic surgeon who can explain these differences to you and help you decide what would be the best option for you. Just don't expect to be wrinkle free with any approach.
Best Procedure to tighten the lower lids
Without seeing a photo of your eyes, it is difficult to know what might be best for you. There are many variables, including age, skin type, available downtime, and actual problem that all help us determine what might be best. One option is laser resurfacing. This helps tighten and smooth the under eye area very nicely.