Why will my toilet not flush after it rains or when ground is wet
Septic System?? If so, the system is FULL of water already and needs to drain out from your drain field.
If it is a municipal system, tree roots CAN SWELL TO 40 % or more of their normal size in wet weather, creating a blockage- hence a slower drainage- I'd look into a rooter service if this is the case and if on a Septic System- even pumping the tank will not help as the ground water is the culprit-preventing more water to disperse.  Pumping the tank will only remove liquid &amp; solids in the inlet side- not removing water from the leach/drain field.