formal or literaryusually written using kana alone
Formal or literary adverb expressing a strong degree of emotion or extent, often used in exclamatory or rhetorical contexts. Similar to どれほど but more elevated.
いかほど is also formal but can be used in more concrete inquiries about quantity or price, whereas いかばかり is almost exclusively used for emotional or abstract extent.
Etymology
Derived from the interrogative いか (how) combined with ばかり (extent, approximately). The exact historical development is uncertain, but it has been used as a formal adverb since classical Japanese.