余(あま)りにSo much...that, (Way) too...

Being the adverbial form of 余(あま)る 'excess', あまりに is a grammar structure that is used to convey an 'excessive' amount of something that caused a certain result. あまりに will almost always be used in sentences expressing some sort of surprise/shock about the degree of (A). Often, あまりに is translated simply as 'so much (A) that (B)', or 'way too much (A)'.

In the last example, we can see that あまり will be followed by の when linked to a noun. Occasionally, にも will be used instead of に. This just emphasizes the 'excess' of (A) further.

As the literal meaning of あまりに is quite close to 'excessively', it may be easier to remember this translation, rather than 'so much (A) that (B)'. Usually, 'it is excessively (A), so (B)' will cover most possible nuances.

Caution

あんまり is a colloquial variant of あまり that is often said, but should be avoided in any form of formal/official writing.