"Emotional heft" refers to the significant emotional impact or weight that something possesses. It implies that a particular thing or experience is deeply moving or has a substantial effect on our feelings or emotions. Full definition
The charm, humor, and emotional heft of Henry made me buy into the premise, and had me believing that anything was possible. (observer.com)
Alice Through the Looking Glass doesn't clear the CGI cobwebs or successfully anchor any of its new events with emotional heft. (slantmagazine.com)
Thanks to a storyline that bestows more humanity on the living objects populating the castle, the supporting cast provides more emotional heft as well. (world.wng.org)