甚 This is shen; CEDict says it’s a variant form of 什. CEDict also says it means: very, extremely, what. But that seems somewhat inaccurate.
Shuo wen jie zi defines 甚 thus:
尤安樂也。尤甘也。引伸凡殊尤皆曰甚。从甘匹。句。匹各本誤甘。依韵會正。常枕切。七部。匹、逗。耦也。說从匹之意。人情所尤安樂者、必在所溺愛也。
Google translate of that says:
You Anle also. Yugan too. The extension of all the specials is very much. From Ganpi. sentence. Peach was wrong. Yi Yun will be right. Often pillow cut. Seven. Horse, tease. Couple also. Said from the meaning of the horse. Those who are more at ease with favors must be spoiled.
Go home google. You’re drunk!
Let’s try baidu:
You anleya. Yuganye. It is said that everything is special. From gumpi. Sentence. Every book is sweet. Yiyun Huizheng. Often occipital cut. Seven. Horse, funny. Couple also. Say from the horse. Those who are especially happy in human relations will be spoiled.
I expected better from you baidu.
Here’s my best attempt. There must be a public domain translation of the shuowen jiezi in English somewhere. However, a brief search has found nothing. If you read this and know of a public domain or open source translation of the shuo wen jie zi into English please comment.
甚 Syn. Peaceful Joy; particularly sweet. Extended to all ordinary things that are said to be particular. [The idea of this character is] From the character for pair. Sentence: Each pair fundamentally errs sweetly. Rhymes with zheng. Header is often cut. 7 brush-strokes. Pair, play. Syn. pair. “To speak” follows from the idea of pair. [Implies] Human emotions which are all happy, and thus also the idea of indulgence.
Here’s what Hanzi Shushu (Richard Searle) thinks:
https://hanziyuan.net/#%E7%94%9A