Why does Chinese sometimes put 儿 after verbs and nouns?
Adding the 儿 to the end of a word is known as 儿化 (er2hua4). Whether or not you use the 儿 really just comes down to regional accents/dialects, but the meaning of the word is unchanged. Generally speaking, northern mandarin dialects use the erhua more than southern ones; in some regions you'll almost never hear anyone use the erhua in speech.

There are some words where the added erhua changes the word's meaning, but these are usually regional/colloquial terms, such as 天儿, which means the same as 天气, not 天.