につき

1. 1Due to; owing to (formal statement of a reason or circumstance, often on signs and notices).Ex. 1
2. 2Per; for each (a rate or amount for every single unit).Ex. 2

The reason sense belongs to formal written Japanese: shop signs, public notices, business announcements and official letters. The rate sense is common in prices, fees and regulations. Compared with everyday ので or general ために, the reason use of につき sounds official and impersonal.

• 1.
  につけN2「につけ」 usually attaches to the dictionary form of verbs like 見る and 聞く, and also appears in 「何かにつけ」, meaning 'every time ..., a certain feeling naturally arises.' The 'per' of 「につき」, by contrast, is a proportional unit that attaches to counters, so the two cannot be interchanged.
• 2.
  ゆえにN1「ゆえに」 only expresses reason or inference; it can follow verbs, adjectives, and nouns, and can also stand alone at the start of a sentence to mean 'therefore.' It has a strong classical flavor and appears mainly in academic papers and legal documents; notices and announcements usually use 「につき」 to state a reason, where 「ゆえに」 is rare.
• 3.
  にてN2「にて」 is the formal equivalent of 「で」, mainly indicating place, means, or a closing such as 「これにて」; in notices it can also express a reason, so 「改装中にて休業」 and 「改装中につき休業」 are interchangeable. It does not express 'per' or 'concerning.'
• 4.
  ごとにN3「ごとに」 corresponds only to the 'every' sense of 「につき」, emphasizing repeated occurrence at fixed intervals of time or distance, or that each unit differs (三十分ごとに来る); it can also attach to the dictionary form of verbs. It has no 'reason' or 'concerning' meaning and is neutral in register.
• 5.
  ためにN4「につき」 and 「ために」 are similar only when expressing a reason: 「につき」 attaches only to nouns and is mostly seen in notices, while 「ために」 can follow verbs, adjectives, or 'noun + の' and is fairly neutral. 「ために」 can also express purpose, and 「につき」 can also mean 'per' and 'concerning.'
• 6.
  のでN5「ので」 is close to 「につき」 only in the reason sense. 「につき」 attaches essentially only to nouns, appears mostly in notices, and sounds formal, whereas 「ので」 can follow verbs and adjectives (with nouns, forms like 「なので」 are used), is neutral in tone, and is common in conversation.

につけ means 'whenever / in connection with' (見るにつけ), and にて is a formal equivalent of で that marks place, means or sometimes cause (病気にて欠席します), but neither expresses a per-unit rate. ゆえに is a literary, logical 'therefore/because', ために and ので are general-purpose reason markers (ので being conversational), and ごとに stresses repetition at each interval rather than a per-unit rate.