Bags under one eye when smile. How to remove?

Better yet, a video demonstrating the problem.  If the problem is present in relaxed position, surgery may be an option. If only when smiling, Botox can help in certain cases.

You need a complete
evaluation by a board-certified dermatologist or plastic surgeon to determine
what options are available to you and for you to make the most educated
decision that will work best for you. We are all asymmetric in some form or
other in the face, and sometimes using topical skin care and some minimally
invasive procedures may improve the situation. If the condition cannot be
handled in this fashion, a surgical procedure may be needed.

The most likely reason for the fact that your two eyes appear different when you smile is that you have a natural asymmetry of your face.  Unless you are gifted like some beautiful models, you will have some asymmetry of your face like the rest of us.  We all have one cheek bone that may be a little fuller, or broader, or flatter than the other, and one forehead bone that may be flatter, or rounder, and so on.  The soft tissues of our face just drape over the bony skeleton, and they will show this asymmetry too.  As we get older and tissues lose volume and elasticity, these asymmetries usually become more apparent.  Thus, in your case, what is most likely going on is that the orbital rim or cheekbone on the one eye is slightly smaller or flatter than the other, and the skin has lost some of its elasticity.  Thus, when you smile and your cheek pad gets pushed up, it pushes the eyelid skin up, and it folds differently over the two cheekbones because there is different support.  This is a slightly different problem than the usual creases that we see around the eyes from muscle activity, like the "crow's feet," and this is very important to understand.  While things like Botox are good for creases caused directly by muscle activity (dynamic creases), it is not effective, and might even be detrimental, for the other kind of creases that  are caused simply by loose skin being "pushed" or folded by movement of adjacent structures.  If you get Botox directly under the eye, your lid could actually droop or you could develop more of a bag from loss of tone; it would be temporary of course, but still no fun.  You may be a candidate for removal of the lax skin and muscle, or you may simply do better with a topical treatment like a laser resurfacing or chemical peel.  Additionally, sometimes the underlying anatomical differences can be addressed or minimized with injections of fillers, or even certain types of implants in select cases.  The bottom line is that you really need a good evaluation by someone who has a good working knowledge of this area so that your specific concerns can be assessed and a proper treatment plan outlined for you.