I moved my almost 6 week old chicks out into their coop with a lamp at night and tomorrow and Sunday its going to be in the upper 60s. Would it be safe to let them out of the coop into the run to check out the grass???
Safe? At that age and those temperatures,Yes. Will they go out? Maybe.
Many chickens don't like change. If they are not used to the run, they may stay in the coop for a couple of days looking out the pop door before they venture out. Or they may all be in the run within 15 minutes. You just don't know how they will react.
I never provide heat to mine after they are 5 weeks old. I don't have Silkies. but last fall I put them out in the unheated grow-out coop when they were 5 and the overnight lows were in the 40's. When they were 5-1/2 weeks old, the overnight low hit the mid 20's Fahrenheit. I have absolutely no worries about your six week old Silkies being in 60 degree weather.