If we keep getting rain a couple times each week, we shouldn’t have to run the irrigation system to keep the grass growing. The downside of getting rain every couple of days is that the grass keeps growing. When the grass grows, it needs to be mowed.
If we have to wait too long between mowing because the rain is coming down or the grass is wet and it gets taller than it should, raise the deck of the mower so you are only removing 1/3 of the leaf blade when mowing. If more than 1/3 of the leaf blade is removed the grass gets stressed and it will take a while for it to recover and start growing again. This brief period of time gives the weeds a chance to get a jump on the grass and become more dominant in the lawn.
After raising the mower deck and mowing the first time, wait about 4 days and lower the mower deck to remove another 1/3 of the leaf blade. This should get the grass back to the height it should be without stressing the grass out and allowing the weeds to take over the lawn.