has a word that gives the nuance that "you do it so much that everything else sort of pales in comparison". It has a negative connotation, meaning it's always a bad thing.

毎日テレビばかり見ている。 Watching television (it is about the only thing you do, you lazy slob).

ヒトリエ uses this word so much in their songs lol. カラノワレモノ

どうしようもない言葉ばかりだ It's just useless words

So much, everything else pales in comparison

it means something keeps going further and further in a negative connotation- It becomes worse and worse. This is more by convention, and not a true grammatical rule however.
In this regard it's different from 一方だ, which can be either positive or negative.

ばかりだ

Used with copula (だ・です)

ガソリンの値段は上がっていくばかりだ。 The price of gas keeps on rising.

日本の人口は減るばかりです。 Japan's population keeps on becoming lower and lower.

最近は全然体を鍛えてないから、筋肉が無くなっていくばかりだ。 Because I have not been exercising my body lately, muscle keeps on disappearing.

観光客が減るばかりで、周りの店が潰れていっている The amount of tourist keeps on decreasing, so stores around here are closing

ばかりで

Similarly, can be used with and (...) (ばかり is a noun, so the 〜て conjugates to で) to denote something is just doing (...) and hardly anything else.

夏は暑いばかりで、楽しくないですよ Summer is just hot, and hardly anything else. it's not enjoyable.

うちの子は毎日遊んでるばかりで勉強をしない。 My kid only plays all day, and hardly anything else and never studies.

この仕事は忙しいばかりで、意味がない。 This job is just busy, and doesn't have much else to it. There is no meaning to it.

ばかりに

Also usable with into (...) to denote thatB only happens because A happens a lot. A bit like から, but only because of one aspect.

背が高いばかりに、写真を撮った。 Just because I am tall, they took pictures.

ボールを投げたばかりに、肩が外れました。 Just by throwing a ball, I dislocated my shoulder.

彼は練習が大変なばかりに、辞めました。 Because the training was only heavy (and not much else), he quit.

Just started doing (...)

日本語を勉強して始めたばかりの大学生ですので、先にひらがなとカタカナを覚えるべきです。 A university student who is just starting to learn japanese should learn hirgana and katakana first.

Recently finished doing (...)

〜た + ばっかり Like "Lately, all I have been doing is (...)". The part where you are now no longer doing it eludes me, but I think it is in the past tense.

きっと名前を聞いたばかりなのに、忘れちゃった。 even though I have recently (finished) heard heard his/her name, I forgot it.

結婚したばかりです。 I recently got married.

日本へ来たばかりの時、日本語が話せなくて困りました。 in the time that I had only recently (finished to) come to Japan, I did not speak japanese and had a hard time.

In-between ている

When used with a 〜ている form, ばかり is often placed in-between.

友達と遊んでばかりいる All I do is playing with friends.

bunpro - ばかりだ jlptsensei.com - ばかりで bunpro - ばかりに