It would seem natural that all languages have diminutives, but how diminutives are formed in different languages must vary considerably. In most cases that I'm aware of in Indo-European languages, the addition of a special suffix denoting smallness or connoting endearment is typical, but in other cases there are more complicated mechanisms at play. The most elaborate system of diminutives I know of is Russian, where common given names are not only made into diminutives in irregular ways, they are then profusely elaborated (with some forms indicating doubled diminutiveness): thus, Aleksander –> Sasha, Sashka, Sashen'ka, Sashechka, Sanya, Shura, Sashok. Keeping track of all these variants was always one of the biggest challenges I faced in reading Russian novels.
Another common way to form diminutives is based on the babbling repetition of syllables when babies learn to talk, and adults mimic them by talking back to them in the same way.
Still today, reduplication and repetition are inculcated in Chinese children from a very young age. Baby talk consists of many reduplicative words, e.g., gou3gou3 狗狗 (“dog”), mao1mao1 貓貓 (“cat”), bao4bao4 抱抱 (“hold [a baby or young child]”). Young Chinese children often have nicknames that consist of repeated syllables, such as Bao3bao, Mao2mao, Ze2ze, Mei4mei, and so forth. They often keep these childhood names even when they grow up, causing others sometimes to do a double-take when they meet an adult with a babyish name. (This occasionally happens in English too, where childhood nicknames carry over into adulthood [e.g., Cappy, Buzzy], but it is hard to think of English childhood names that consist of repeated syllables, whereas this is extremely common in Chinese.
I myself went through three distinct stages in the development of my name: Vicky [from birth through elementary school and middle school], Vic [high school and college], Victor [after college until the present time]; however, I am still “Vic” to family members and a few very close friends, though some of them have also taken to calling me Victor as a sign of respect. Although no one ever called me VicVic, interestingly one of my nieces did call me VicBic before she went to elementary school. Many of my Chinese undergraduate and graduate students, especially girls, have reduplicated names: Jiajia, Lala, Zhenzhen, but boys do too: Binbin.
Chinese is permeated with reduplicatives, and not just for the purpose of forming diminutives. Here are just a few examples:
kànkàn 看看 ("have / take a look")
guāiguāi 乖乖 ("nice; obedient; well-behaved; darling; lambkin")
gāogāoxìngxìng 高高兴兴 ("gleeful; cheerful; really happy")
mǎmǎhǔhǔ 馬馬虎虎 ("so-so; careless; casual")
Perhaps the most famous contemporary instance of a Chinese reduplicated baby name that has carried on into adulthood is that of Bo Guagua ("Melon-Melon"), the son of the disgraced Chinese politician, Bo Xilai.
Bó Guāguā 薄瓜瓜
Báo Xīlái 薄熙來
Of course, not all duplicative terms in Chinese are diminutives, e.g.:
shūshu 叔叔 ("uncle; father's younger brother")
jiùjiu 舅舅 ("uncle; mother's brother")
gūgū 姑姑 ("aunt[ie]; father's sister")
— unless we interpret them as being spoken from the point of view of a child.
Here are a couple of scholarly references to literary and linguistic aspects of repetition in Chinese:
Cecile Chu-Chin Sun, The Poetics of Repetition in English and Chinese Lyric Poetry (Chicago: Chicago University Press, 2011)
Perry Link, An Anatomy of Chinese: Rhythm, Metaphor, Politics (Cambridge, MA: Harvard University Press, 2013), esp. pp. 191-93.
A full explanation for the high degree of repetitiousness (both near and exact) in Chinese poetry (and in Chinese more generally) would require the writing of an entire thesis and entail recourse to analytical methods drawn from a wide variety of fields, subfields, and disciplines, including grammar, syntax, phonology, psychology, cultural studies, and even cybernetics (which pays careful attention to redundancy). I venture to say, however, that in the final analysis, the main reasons for the frequent resort to repetition in Chinese poetry and in Chinese discourse more generally are directly or indirectly linked to the unique (in today’s world) writing system.