Well I'm looking back on your threads and it looks like this tank has only been set up since February.. about a month and a half ago.
Since you don't own a water kit you have no way of knowing if this is fully cycled and cycling can take up to two months. If you have been doing only 50% weekly this whole time your boy has had to suffer through very high ammonia and nitrite spikes and this is the cause of his popeye.
You needed to (and still do) be testing daily with a reliable drops kit for ammonia and nitrite and doing an extra 50% change any time you see either. show up, even as little as .25ppm. In addition to this a weekly 50% with siphon is needed to remove poop and other debris from the gravel. It is not enough to just scoop water off the top ever.
First you will see ammonia, then nitrite. Eventually, hopefully, you will see ammonia fall and stay at 0 even after a week of no water changes, and finally nitrite. At this point you will be left with only nitrates after a full week of no changes and these can be kept <20ppm by weekly 50% change with siphon.
My last concern is what filter you are using and how you maintain it? The problem with filters for small tank is they often only contain one type of media. That media must be replaced monthly because of the carbon addition, but replacing all media at the same time will wipe our most of your biofiler and restart your cycle. Your filter may need some modifying as well
At this point I would do a series of 3 50% water changes back to back, an hour a part. Then get a test kit and keep up on your changes. Do all changes like this and you won't shock him:
The 50% changes the betta can be kept in the bowl and use a turkey baster to remove half the water and as much of the debris as possible. For the 100% you need to remove him - scoop him out with a plastic solo type cup and set aside while you thoroughly rinse the bowl and gravel to remove the debris. Then he should be acclimated to the new water by floating for an hour while you slowly add a couple tablespoons of new water to the cup every 10 minutes. When you release him, try to let as little of the old cup water back into the tank as possible. All water changes should use same temp water, matched to running tap using the in tank thermometer and the water needs to be premixed with conditioner before adding it to the betta tank. If you don't already have anything, you can use gallon water jugs from the grocery store - rinsed thoroughly in hot water but no chems.
I would also get some epsom salts - 100% pure magnesium sulfate with no additives of any kind. I get mine at CVS Pharmacy. You should predissolve it outside the tank at 1 tsp per gallon and add slowly over an hour. Salts do not evaporate or break down, so you only need to add more along with a water change, and then only add back as much as water you remove/replace. Leave him in the salts 2 weeks. Then you can discontinue adding them along with a water change and phase them out slowly like that.
The increased water changes, closer monitoring of cycling, potentially modifying of his filter, and epsom salts will hopefully be all that's needed. Sometimes there is a residual infection from this as well, but since his eye is still clear hopefully no more will be needed