You must not use pure distilled water.
Distilled water has no buffering agents which means the pH will continue to drop after it's added. That is very stressful to your betta.
If you must use purified water then you need to buy something like Kent Marine RO Right to get the water buffered so the pH will remain stable. It will also add other stuff that is important to the health of your fish. There are other ways to buffer the water, but this is by far the easiest.
There is also no reason to let distilled water sit since it has already been purified and contains no chlorine. If you use tapwater, or any other water source containing chlorine you'll have to dechlorinate or age the water.
How much water do you change weekly? If the tank contains no filtration then it would be best to change out nearly 100% of the water, or else you will only be removing part of the waste and it will continue to build up.
It is best, as already mentioned, to test for Ammonia, nitrites, nitrates and pH. Idealistically ammonia and nitrites should always be 0. Nitrates should be below .40.
In an unfiltered tank you at least want to keep your ammonia below .25, and much lower if possible.