bakari is a "completed fullness", for instance that's all you got because with that you didn't need any more. dake means that's all you got, but more would be better/ok/possible/,,,
I second KWhazit's comment: there are most definitely two separate entries here. Also need to beware: depending on meaning ("just happened"/"nothing but"), placement is different: 食べたばかり -> I just ate (moments ago). ばかり食べた -> All I/we/etc did was eating (and nothing else). Furthermore, I believe pronunciation/spelling: ばっかり is also valid (very often heard in speech).
#5018 その本を買ったばかりです。 #5019 昨日アメリカから帰ってきたばかりです。 I just got back from the US yesterday. #5027 Use kanji. 彼は昨夜ここに到着したばかりです。 #5028 かわいそうにその少女は一日中泣いてばかりいました。 #5029 この古い車はいつも壊れてばかりです。 #5032 Put "、" right after "〜いるので."
How is this different from 'dake' or 'tada'?
I think this needs to be split into two separate entries. ばかり (after a past-tense verb) in [#5018], [#5027], [#5034], and others, means that something has only just happened ばかり (after a noun, -te form verb, etc.) in many of the other examples ([#5021], [#5028], [#5031], etc.) is more of a "nothing but", "all it ever does is", or "all that's there is" feeling.
１．正しいことばかり選べないそれくらいわかってる。 Meaning something like I can't make but the wrong choice. ~ばかり ~てばかり ２．着いたばかり。 I just arrived. ~たばかり