I then rounded the temperature to the nearest degree Celsius and plotted the average humidity for each rounded temperature:
This "trilinear" function fits the data fairly well:
$-0.0135991 \left| x-21 \right|-0.00131261 \left| x-1 \right|-0.0075821 x+0.899765$
I still need to look at standard deviation for each point and do many other things, continuing work at https://github.com/barrycarter/bcapps/blob/master/STACK/bc-nj-temp-hum.m
In the summer though, as temps go up, there will also be changes in weather patterns, with a higher portion of you air masses coming from the gulf or even straight up the coast. These will be wetter air masses. In addition, now you are getting a cooling effect from the ocean. Yes, temps are higher, but still a few degrees lower than they likely would have been without the ocean effect, and cooler than what they likely are to your West. Drop the temp of the air mass a couple degrees and the relative humidity rises.
One more factor in that line, when the air mass is coming more directly from the West, or from the NW, it crosses a line of mountains before it gets to NJ, which will tend to cause more of the moisture to precipitate out. With the summer pattern, with a bit more of the air being gulf and coastal, this misses some of the effect of NJ being on the lee side of a range.
Not saying these are the cause, but logically, they likely seem to contribute to a correlation between seemingly higher humidity as temps increase.