In cooler months, augment the shirt with a synthetic wicking under layer . I prefer a long-sleeved top with a zipper neck. The neck zipper makes it more useful across a broader range of temperatures. Simply zip or unzip the neck to accommodate changing temperature levels. A 200 weight full-zip fleece sweater provides welcome warmth in the cooler months.
Fleece is relatively light and dries fast.
A fleece sweater also makes a great pillow. Add a waterproof windproof breathable shell when hiking the Canyon in the fall through early spring. The shell will provide relief from the wind and protection from the occasional rain or snow shower. It is unlikely you will need a shell in the summer though you may appreciate one when near the rim. The shell should be light in weight and large enough to go over all your layers.