余(あま)りSo much...that

Both express emphasis, but in different ways. あまり is a noun that emphasizes an extreme degree leading to an unintended result, e.g. 悲しみのあまり泣き出した ('She burst into tears from too much sadness.') こそ is a particle that stresses importance or exclusivity, e.g. 今日こそ早く寝よう ('Today, for sure, I'll go to bed early.')

Both すぎる and あまり express that something is excessive, but they differ in usage and nuance. すぎる attaches to the stem of verbs and adjectives, while あまり follows plain-form verbs, nouns with の, or な-adjectives with な. Though すぎる can imply something negative, あまり more clearly emphasizes that the excess leads to a negative consequence.

あまり follows a noun or verb phrase and shows that an extreme state leads to an unintended result, e.g. 緊張のあまり声が出なかった ('I was so nervous I couldn't speak.') からこそ attaches after the reason and emphasizes it as the precise cause, e.g. 緊張したからこそ全力を出せた ('It was precisely because I was nervous that I gave it my all.')

Both mean 'too much', but differ in nuance. あまりに emphasizes intensity and doesn't necessarily imply a result, e.g. あまりに暑い日だった ('It was an extremely hot day.') あまり highlights excess that leads to a (usually undesirable) outcome, e.g. 暑さのあまり眠れなかった ('I couldn't sleep due to the extreme heat.')

Both emphasize extremity, but with different focuses. Adjective + 限りだ expresses a strong feeling at its peak, e.g. 悲しい限りだ ('I'm as sad as can be.') あまり indicates that excess leads to a (usually undesirable) result, e.g. 悲しみのあまり声が出なかった ('I couldn't speak due to extreme sadness.')

Both express degree, but with different implications. なかなか implies something is quite or unexpectedly good, e.g. なかなかいい店だね ('This place is surprisingly good.') あまり highlights an excessive degree that leads to an unintended or negative result, e.g. 緊張のあまり声が震えた ('I was so nervous my voice shook.')

あまり has the base meaning of 'excess', but its nuance changes with context. Together with a negative word in the form あまり～ない, it means 'not very (A)', e.g. あまり寒くない ('It's not very cold.'). Used affirmatively, it implies something of an excessive degree, e.g. 緊張のあまりうまくできなかった ('I was so nervous I couldn't do it well.').