に就(つ)きDue to, On account of, Each or every

Both are formal expressions where one condition influences another, but with different nuance. につき means on account of or due to, as in 雨天につき中止になる (Cancelled due to rain). にあたり・にあたって means on the occasion of or at the time of, as in 退職にあたり一言挨拶をする (Say a few words on the occasion of retiring).

These expressions are loosely related in that both indicate a reason. ばかりに conveys that a specific cause led to a negative outcome, often with a nuance of regret, e.g. 忘れ物をしたばかりに受験できなかった ('Just because I forgot something, I couldn't take the exam'). につき, by contrast, is a formal, neutral expression often used in official contexts, e.g. 工事中につき通行止め ('Road closed due to construction').

Though similar in that both use に with a form of the verb つく, these patterns differ in meaning and formality level. について means 'concerning (A)' and typically marks the topic of a discussion, question, or so forth, e.g. 日本文化について話す ('Talk about Japanese culture'), while につき is a formal way to express a reason or condition, often used in official announcements, e.g. 悪天候につき中止する ('Cancel due to bad weather').

Both ために and につき can express 'due to (A)', but differ in tone and usage. ために requires の to connect to nouns, e.g. 悪天候のため ('Due to bad weather') につき connects directly and sounds stiffer or more formal, e.g. 悪天候につき (Same meaning) Unlike ために, につき cannot be used to express purpose.

Both express cause, but differ in tone and formality. おかげで implies a positive result with gratitude, e.g. 先生のおかげで合格できました ('Thanks to my teacher, I passed.') につき states a neutral reason, often used in formal notices, e.g. 雨天につき中止します ('Due to rain, it is canceled.') It also only follows nouns.

まい～のように and につき both express frequency, but in different ways. まい～のように is used with 'every~' time expressions to mean 'almost every (A)', e.g. 毎日のように 'almost every day'. In contrast, につき follows time/quantity expressions to mean 'each' or 'every,' e.g. 30分につき 'for every 30 minutes'. につき can also mean 'due to', which is unrelated to frequency.

Both せいで and につき express cause, but with different nuance and tone. せいで is more colloquial and typically introduces a cause for a negative result, e.g. 雨のせいで試合が中止になった ('The game was canceled because of the rain.'). につき states a reason more neutrally and is often used in formal written announcements, e.g. 工事中につき通行止め ('Closed to traffic due to construction.').