Why does relative humidity seem to correlate with high temperature (at least where I live)?
In coastal New Jersey, relative humidity is maximal in the early fall when the ocean temperature is warmest, and minimal in early spring when the ocean is coldest.  However, the monthly variation is rather small:  

Atlantic City, New Jersey:  

70 January
69 February
67 March
66 April
71 May
73 June
74 July
76 August
76 September
75 October
73 November
71 December
72 Annual 

Newark, New Jersey  

65 January
63 February
60 March
58 April
62 May
63 June
63 July
66 August
68 September
66 October
67 November
67 December
64 Annual 

source: https://www.currentresults.com/Weather/New-Jersey/humidity-by-month.php