We're supposed to get a big rain storm tonight. When we got home this afternoon, we checked the weather station and:
The dot next to the second line was our starting point, when the weather was clear. The straw went down more than an inch as the air inside the jar expanded, which means the pressure dropped (the balloon puffed up and out because of the increase in pressure in the jar).
The water level in the other barometer rose slightly as well, but definitely not as noticeable as the straw.