[noun] + ばかり [verb て-form] + ばかりいる [verb た-form] + ばかり [noun (number)] + ばかり
ばかり after a noun means "nothing but", "only": that one thing, again and again, usually more of it than there should be. It takes the place of が or を, and it often sounds like a complaint.
Other particles stay, and usually go in front of ばかり.
The form of the verb decides the meaning, and each is its own grammar point. The て-form with いる is "does nothing but". The た-form is "has only just done".
たばかり is about how recent it feels to you, so it can stretch to weeks or months: きょねん去年けっこん結婚したばかりです.
These go beyond "nothing but".
In casual speech ばかり is often said ばっかり, or ばっか.
After a number, ばかり means "about". This is written or formal; in conversation you say くらい or ぐらい.