I suppose this gets into the question of "what is a god" then.
Now, I will admit it may not have been clear that I was combining some concepts in my initial post, so let me first go ahead and make explicitly sure to decouple them. Many real-world mythologies involve the food of the Gods being special. For example, in the Norse Pantheon the Aesir and the Vanir eat the Apples of Idun, which restore their youth and vitality. Without the Apples, the gods would die of old age and sickness. In fact, when they lost access to the Apples, they quickly began to age. Similar stories revolve around Ambrosia from Ancient Greece which in the Illiad is used by Hera and allowed her to "cleansed all defilement from her lovely flesh", Peaches of Immortality from Chinese Myth cover again a similar vein. Now, not all godly power derives from these foods, but the immortality of the gods does, and that is a key point for many on "what is a god".
Now, I have read many stories that take that concept and combine it with another concept. Particularly in Japanese myth, but I believe also in Hindu belief, the food ritually offered at shrines is considered empowered by the faith of those offering it, and becomes the food of the gods. This could have also been a Sumerian belief, but I'm really out of touch with my Sumerian mythology research. And so some people in various stories have stated that it is faith that powers these foods, and therefore faith which grants immortality to the gods.
I also find your mention of gravity as... not quite accurate. You can't stab gravity, but you can stab the Gods. In fact, in the Illiad, Aphrodite is wounded by a spear thrown by Diomedes. You can also bind the Gods, as Hera was famously bound multiple times in Greek Myths (once from Golden Chains in the heavens for betraying Zeus, once in a throne forged for her by Hephaestus, and I believe a third time). The concept of Gravity might not need worship to continue, but it also cannot be "killed". Yet, the Gods can be killed, injured, bound, ect so therefore it could be that they need sustenance to continue, and that sustenance could be special because it is powered by Faith.