I would recommend an in-person consultation with an experienced and board-certified oculofacial plastic surgeon who will be able to thoroughly assess your lids/anatomy and discuss treatment options with you. Definitely do your homework, try to get more than one opinion, and good luck.
For four weeks out from surgery, it appears as though your lids are healing nicely and your closure looks good. As others have mentioned, incomplete closure is very common for the first few weeks after surgery. You would notice eye irritation, burning, pain, blurriness, etc if the incomplete closure was significant enough to cause problems. Topical lubrication with artificial tears and sometimes ointments can be helpful in those cases. As always, you should contact your surgeon when you have specific concerns or questions about your recovery. Good luck!