Due to a toasty weather, spring and autumn is the best time to visit the Jordan. These periods are not too hot for trail hiking, visiting Petra and enjoying the Dead Sea. As a drawback, you will have a desert wind regularly blowing from March through June. If you want to learn more about Muslim traditions, plan to arrive during Ramadan.
Summer can be comfortable on elevations with cooler breezes but is a bit suffering in Aqaba due to the unbearable hot wind. You can taste nutritious camel milk and stodge watermelons. October can welcome you with rains, but otherwise the weather is pretty pleasant. Sharp and short showers fall mostly in the winter which can be unexpectedly cold.