I've often heard some of my German friends use the ending "-chen" when talking, in an informal manner. For example, "Hallöchen", "Kärtchen", "Liebchen", etc ... Formally one would say "Hallo/Guten Tag" and etc ... I'm just curious why some of the words can be informally said in such a manner.
As amadeusamadeus points out, the suffix "chen" gives the diminutive form of a noun. But that is not the whole story.
There are some nouns like "Mädchen" which are no diminutives. Note that this example is etymologically a diminutive form of "Magd" (maid), but is no longer understood as a diminutive. It means "girl" or "maid". Another example is "Liebchen" which is not the diminutive form of "Liebe" but means "sweetheart" or "darling". It may also have a negative connotation ("Verbrecherliebchen").
"Hallöchen" is a joke form for "Hallo". It is not really a diminutive because "Hallo" is not a noun. An extreme variant is "Hallöchen Popöchen" which is used by some people who believe it is witty but which actually gets on the nerves of their audience.
Some formal diminutives change the meaning of the original noun. For example, "Freundchen" is not a little friend, but it is used if you wag your finger to other people. A similar example is "Bürschchen".
You see that there are various reasons for the occurence of the ending "chen". In most cases it indicates that something is a small (Haus / Häuschen) or not full-grown specimen (Katze / Kätzchen). It may also be used as an affectionate form. In other cases it is just a joke. And there are cases where the "chen" is an intrinsic part of a word and does not belittle something else.
These could be different endings. Something being labeled diminutive is a good indicator that the original function had been lost. I believe there's no good complete etymology for this suffix. The question why people perceive diminutives would be for a linguist to answer. So the question is entirely too broad.
One notable influence at least might be usage in names, that are not regular parts of speech, but colloquially given and thus potentially irregular, from there taken on to proper nouns, etc., etc.
For hallo ~ hallöchen, the etymology is not clear. French hola could have la as determiner, cp. hey there; Middle English hey lo might be explained from "look"--when and if this k elided, it would have resembled -gh ~ -ch, the -n might be excrescent, thus a low German form; euch "you" as a vocative determiner can be seen in Hallo euch. Old High German hat holan as verb; it's not necessarily that this had been used exclusively in imperative hola!. The ending -en gives it a kind of nominative plural aspect (cp. Grüße, mit freundlichen Grüßen although one could understand grüße dein Vectory "sincerly yours" also as imperative, "greet me"). Hallöle (*-le also often diminutive) might be from like, likewise (whence -lich, En. adverbial -ly; cp further Latin alis). One can only speculate.
There might also be remnants of an old dual, in spirit. The grammatical dual dumber is explained very well by @Schölnast here.
So, all these might be regional and colloquial. This should count as a general example. Sometimes the diminutive may be constructed intentionally (perhaps for Liebchen, but I wouldn't be), probably in the majority of cases today, but this option might obscure older roots. For the usual speaker who simply reitterates heard idioms, like me, without any indepth study of the etymology, it depends all on context.