I'm not entirely sure why else Maya would like them so much.
Wild guesses that sometimes touch upon various theories:
1) Watermelons are not a native fruit to Japan, so it could be symbolizing that Maya is not native to this world, or that she's in love from something not from her world.
2) The gifting of fruit, and watermelons in particular, is a cultural thing in Japan. It could be symbolising that Maya herself is a gift (presumably to Akira)
3) In some areas, watermelons symbolize love and fertility, and perhaps this is why Maya jumped to the "Akira got Ayane pregnant" assumption -- because she's pregnant. It would explain her eating habits.
4) It could be a very mundane thing, and Akira just had watermelon on hand during lessons, so they've become a symbol of a happier time in her life.
Maya wearing a melon rind as a helmet makes me think we're meant to assume that the watermelon represents what Maya IS as much as it being a personality trait of hers. And with all the melon-fucking going around...
Reasonable (to me) but still very likely false conclusion: Maya is Young Maya, part of the Maya Trinity with Long Maya (representing motherhood and middle age) and Moyo (representing old age and death). Young Maya represents fertility and youth, and thus the watermelon. In abandoning her post, she has inadvertently fucked the natural order. The loops are a side-effect, potentially, and every time "she resets the world" she's basically choosing to stay, and that the only way to break the cycle is to return to her post and restore the natural order. The half-eaten watermelons are children who never got to be born. Maybe they're Akira's children, unmade by innumerable resets, maybe they're consumed by one of the other Old Gods that Akira seems to have become aware of.
Some of that might be a reach, tho. I am quite prone to the overthink.