あまり（に） details

high + so much so that — an extreme degree brings about the result that follows

takai amari ni

so much so that — an extreme degree brings about the result that follows

彼かれは焦あせるあまりに、財布さいふをどこかに置おき忘わすれてしまった。

kare wa aseru amari ni, saifu o dokoka ni okiwasurete shimatta.

He was so flustered that he ended up leaving his wallet somewhere. neutral

忙いそがしさのあまり、食事しょくじをとるのも忘わすれてしまった。

isogashisa no amari, shokuji o toru no mo wasurete shimatta.

I was so busy that I even forgot to eat. neutral

Examples

so much so that; out of sheer X — an extreme degree of something directly causes the result that follows

彼かれは焦あせるあまりに、財布さいふをどこかに置おき忘わすれてしまった。

kare wa aseru amari ni, saifu o dokoka ni okiwasurete shimatta.

He was so flustered that he ended up leaving his wallet somewhere. neutral

忙いそがしさのあまり、食事しょくじをとるのも忘わすれてしまった。

isogashisa no amari, shokuji o toru no mo wasurete shimatta.

I was so busy that I even forgot to eat. neutral

あまりの物価ぶっか高だかに、生活せいかつが苦くるしくなっている家庭かていも少すくなくありません。

amari no bukka daka ni, seikatsu ga kurushiku natte iru katei mo sukunaku arimasen.

With prices rising so steeply, no small number of households are finding daily life difficult. formal

plain clause (mostly psych/emotion verbs and verb-ta) + あまり(に)attaches to plain clause
{I}あまりにattaches to i-adjective
{NA-stem}なあまりにattaches to na-adjective
{N}のあまりにattaches to noun

あまり — に often drops with no change in meaning, especially in speech — 緊張きんちょうするあまり、頭あたまが真まっ白しろになった。

あまりの＋Nに fronts the noun row (あまりの物価高に), the mirror image of
Nのあまりに — both are attested, and the fronted shape reads more written.

すぎる
すぎる suffixes straight onto the stem and describes the excess as a property of that one word alone (心配しんぱいしすぎる "worry too much"), needing no second clause; あまりに stands apart from the word and frames the whole preceding clause as the CAUSE of a separate result clause (心配しんぱいするあまり、眠ねむれなくなった), and always leads to one.
ほど
ほど illustrates a degree through a benchmark comparison, often hypothetical (死しぬほど疲つかれた — not literally dying); あまりに names the excess as the direct, actually-occurred CAUSE of the result clause (緊張きんちょうしたあまりに、声こえが震ふるえた really happened because of it), not an illustrative simile.

Pattern	Attaches to
すぎる