This is not caused by obesity in this case but by inflammation of the turret conjunctiva. This can be caused by a piece of shed in the turret or other foreign material such a particulate matter from vines, sap from plants, or substrate, or an early respiratory infection. Hypovitaminosis A can also be at work given that it’s both eyes affected as it can cause respiratory epithelium to be abnormally thickened (hyperkeratosis) which impedes normal drainage of fluids and debris from the turret through the nasolacrimal duct. As the fluid backs up it causes inflammation and can lead to infection. Sometimes even “pearls” of debris form in the saggy portion of the turret that have to be removed. The most effective course of action is to go to a reptile vet so they can flush the turret out, hopefully dislodging any foreign material that may be residing in there, making sure the nasolacrimal duct is patent, and starting antibacterial and anti inflammatory ointment. These can be difficult to treat if they progress. Treating it now before it worsens is the best time to do it. Sometimes flushing is needed several times and even systemic medications in addition to topicals. Increase misting and if he is rubbing his face on those vines (because these itch and are uncomfortable) it should be removed or wrapped because small bits can flake off when it’s rubbed. Disinfect any misting apparatus you make sure they are clean and not further contributing to the problem by spraying any mold or bacteria into the eyes.