日ひに日ひに

日ひに日ひに〈形けい容よう詞し〉くなるto become increasingly ~ day by day
秋あきになって、日ひに日ひに寒さむくなってきた。
Now that it's autumn, it's getting colder day by day.
日ひに日ひに〈動どう詞し〉ていくto keep doing ~ more and more each day
赤あかちゃんは日ひに日ひに大おおきくなっていく。
The baby is growing bigger day by day.
日ひに日ひに回かい復ふくするto recover a little more each day
祖そ父ふの体たい調ちょうは日ひに日ひに回かい復ふくしている。
My grandfather's health is improving day by day.

Kanji

日ひ々びN1sense 1
日々 usually means 'day after day' in a neutral, ongoing sense, while 日に日に stresses a visible change that grows or shrinks with each passing day.
徐じょ々じょにN3sense 1
徐々に means 'gradually' over an unspecified span of time, whereas 日に日に specifically ties the gradual change to each individual day.
次し第だいにN2sense 1
次第に describes a gradual progression like 日に日に, but it doesn't carry the day-by-day imagery and can describe change over any timescale.
日ひ増ましにN1
日に日に and 日増しに both mean 'day by day', but 日増しに sounds slightly more literary and emphasizes the cumulative, incremental nature of the change.

Reduplication of 日 (hi, 'day') with the particle に, literally 'day by day'. The form is straightforward and transparent.