Let's examine this issue by looking at trends of dew point, which is probably the best measure of stickiness and unpleasantly moist conditions. Dew point, the temperature at which the air becomes saturated when it is cooled, is a good measure of the amount of water vapor in the air. If there is more moisture, you don't have to cool as much to get saturation. Thus, high dew points mean more water vapor in the atmosphere. When dew point gets into the 60s F, we start to feel uncomfortable. 70s is unpleasant. 80s are oppressive.
A longer period plot (35 years) for summer dew point at Seattle is shown below. Again no trend.
What about Yakima, along the eastern slopes of the Cascades during the past two decades? As shown below, there is no temporal trend there either.
Next, let's consider summer precipitation, could that be increasing? More humidity might be expected to enhance rainfall. Here is plot of Washington State precipitation over the last century--no apparent trend is obvious. During the past 30 years, there has been a drying trend, if anything.
The bottom line of the above information is that there is really no evidence that Pacific Northwest summers have been getting more humid.