How does it work?
The candle needs oxygen to burn. When you cover the burning candle with the jar, the flame eventually goes out as soon as all of the oxygen is used up. Since there is no more oxygen under the jar, the rest of the gases (nitrogen, argon, carbon dioxide, and others) exert less pressure than the atmospheric air. The greater atmospheric pressure on the outside of the bottle pushes the water in the pan up into the bottle.
There is another important factor that accounts for the rise in water level. The candle flame heats the air in the bottle, and this hot air expands. Some of the expanding air escapes out from under the bottle — you might see some bubbles. When the flame goes out, the air in the jar cools down and the cooler air contracts. The contraction of the air draws the water up into the bottle.
My understanding is different than yours. I believe that every O2 burned is replaced by a CO2 so there should be no significant pressure change from burning O2. This can be seen because the water rises only as the candle is going out and the air is cooling and most of the rise happens after the candle is out all together - when no O2 is being burned. The air expansion is responsible for nearly all the water rising and the water is not "drawn" up as you describe, but pushed in from the outside by the air pressure. An interesting related experiment is to rust some steel wool in the top of the bottle which should indeed result in rising water because O2 is being chemically combined with the iron.
I agree that the heat from the candle causes the gas in the bottle to expand which causes some air to escape which is what may cause the bubbles to form under the bottle. I also agree that when it begins to cool the pressure caused by the heated gas goes down. BUT when the candle burns it not only produces CO2 it also produces water vapor which I have seen condense on the side...SO not all of the O2 goes into the CO2 it goes in to Water as well which occupies less volume. Either way I think the rise in water has to do with the difference in pressure outside vs inside...like a Hg barometer

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