I have read over and over again how low KH (mine is 2 dH) will make pH swing wildly and stress your fish.
This is false information, unfortunately still be bandied about by individuals who either have no understanding of the issue, or are misleading without really knowing it--i suppose those are the same issue. It all depends upon the fish, and the GH/KH/pH of the source water. If one has fish species requiring harder water and a basic pH to function well, then obviously one does want a higher pH and sufficient buffering to keep it steady. Increasing the GH/KH is the only safe way to do this, if the sou4rce water is too soft to begin with. But this applies to fish requiring such water.
At the other end of the issue are the soft and very soft water fish. Most of these are best in zero GH/KH, with an acidic pH. The water chemistry of any aquarium will stabilize as the biological system becomes established. Leaving it alone will allow the natural laws of chemistry, biology, etc. to work properly, and all will be well. As soon as the aquarist begins fussing with attempts to change KH or pH, the result is usually disaster with pH crashes, stressed fish, etc. Now this is very general, but it is still the basic premise.
I've been keeping my tank for around 2 months now without issues in terms of fish health. I tested pH week on week and both times read 6.4. 6.6 from the tap should keep it staple with weekly water changes right?
Yes. The pH may lower over time, just let it do what it wants.
My water is zero GH/KH, and I keep only very soft water species. I had 8 tanks in my former fish room before I had to downsize when I moved two years ago, and each tank established a biological system that was very stable for years, well over ten. The pH settled out at "x" in each tank, one tank was 6.2, another below 5, etc. I did weekly 60% water changes with tap water (zero GH/KH) and I never saw any fluctuation over more than a decade of initially weekly, then monthly, then sporadic tests of pH and nitrate. Those were stable biological systems, suited to the fish. Back in the 1980's I had a tank of mollies, and used a calcareous substrate (dolomite) to increase GH/KH/pH because that species needs it.