Will dissolving my overfilled right eye cause premature sagging and wrinkling in that area?

Hyaluronidase will have best effects for over-treated areas when applied within a couple months post-HA filler injection. Hyaluronidase will not cause sagging of the skin. Patients who have been over-injected often fear that all of their filler will be removed after having Hyaluronidase or that they will appear diveted and depleted. This is not necessarily true if injecting with an experienced injector who can evenly spread hyaluronidase in targeted areas. I recommend that you seek in-person consultation with an experienced injector.Best, Dr. Anil Shah

The advantage of using a hyaluronic acid-based fillers is that the filler can be dissolved if the result is not what was anticipated or if there is some form of adverse reaction. The general claim that hyaluronidase only dissolves injected hyaluronic acid and does not dissolve surrounding native hyaluronic acid flies in the face of some very important facts. For one thing, before hyaluronidase was ever used for dissolving injectable fillers, it was used in normal tissue to help disperse other medications. What's more, recently, it was used successfully for softening tissues around the mouth (in order to permit greater mouth mobility) in patients with scleroderma (where no hyaluronic acid was injected). And I have personally used hyaluronidase successfully to help shrink tissues, such as excess fat under the chin. So, the short answer to your question is that it is possible that there may be some additional laxity in the region where the hyaluronic acid is dissolved. The good news is that a skilled, experienced physician injector will very likely be able to re-treat the region properly with filler to achieve the results you originally desired. Make sure that you consult with a board certified aesthetic physician and be certain to ask to see his/her personal before and after photos. Best of luck to you. 

Combining hyaluronidase to dissolve the filler with a skin tightening procedure would be optimal for the reason you describe.  My suggestion is Plasma Pen which is very effective in tightening lower eyelid skin.