My guess on this is the following. Assume that the dew point is 70 and the temp at 6 AM is also 70. Hence, the relative humidity is 100%. As the temp rises as the sun rises, the temp climbs but the dew point remains 70. Hence, the relative humidity drops and it does not feel as muggy.
So you are saying it feels muggier because it is muggier?
No doubt this is true, at those places and times where and when it is muggier in the morning.
Next up: Why does Houston feel muggier than Phoenix? 
Why is it muggier is the question.
To be fair, that was not the question. That is a new question.