I also have a small head like a 6 7/8" size when buying a fitted hat. Which is Super hard to find so i usually buy a 7 and its big
. For running i always buy adjustable hats so i can make them smaller. I have one of the run disney nike ones i use for all seasons except summer (and i have it basically as tight as it can go). For summer months i wear a north face vented hiking hat (also as tight as it gets) but that one is a bit nicer fit cause it is packable so its soft and a little more form fitting.