私はあまりまめに書きませんが、ことばを学ぶのは大好きです。
I don't write that well, but I love learning the language.
What is the etymology of the word まめ here and what specifically does it mean?
My friend gave me this explanation:
「まめに書きません」＝そんなによく書きません、あまり書きません、規則正しく書きません.
まめに働きます＝まじめに一生懸命働きます」という言い方もあります。
I guess まめ is a colloquial word meaning to do well or do diligently?
mame (ni) expresses the way in which one seriously works hard at something without complaining about the task. Often you may translate it as "diligent(ly)".
There is another common usage meaning "healthy" as in mame ni kurasu "to live healthy".
You may see it written as 忠実 or 実.
The word is not new; it's been around for many hundreds of years, so I would not say that it is slang.
As Dono explains, this can mean "diligent; serious; hardworking; hale, healthy".
Although this has the same kana reading as 豆{まめ} "bean", it isn't the same word. "Bean" is pronounced with a high second mora and then an immediate drop, as in まめは【LHL】, while "serious" is pronounced with the so-called heiban or "flat" pitch accent, where the pitch rises on the second mora and then gradually comes down, as in まめに【LHH】.
Derivationally, Shogakukan states that mame "serious" is probably an alteration from 真{ま} ("real, true") + 実{み} ("body, content; fruit, results"), or from 真{ま} ("real, true") + 目{め} ("eye; appearance"). Meanwhile, the entry at nihonjiten.com suggests a shift from 真{ま} ("real, true") + 実{み} ("body, content; fruit, results"), an abbreviation of 真面目{まじめ} ("serious"), or a shift from 正{ま} (irregular reading, "real, true") + 身 ("body, content"). Dropping out the じ from the middle of まじめ seems unlikely to me, so the other theories are probably closer to the root of the matter.
As Dono notes, まめ in this sense has been in use for a long time. Its earliest appearances are probably in the Nihon Shoki, finished some time around 720 CE. In section 11 of volume 14 about Emperor Yūryaku, we find the following text:
This is in 漢文{かんぶん}, which is essentially Classical Chinese, so I'm unsure of the meaning, but it seems to be "seriously shining sun" or something to that effect. At any rate, this まめ does appear to be the same word, indicating a very long history in the language. As Dono notes, this is not slang.
