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I find it helpful (and fun) to learn a group of words that are connected
etymologically. For example, the stem うら(裏、心) is related to so many words
ranging from JLPT N1 to N5 including:

  * うら(裏)
  * 憂う
  * 嬉しい
  * 羨ましい （うら やむ し）
  * 占う （one of the many なう words）
  * 恨む

On the other hand, there are many words that can be seen as the stem + なう，the
most common of which being 行う, which is intrinsically related to 起こる via the
stem.

Some other なう words that are intrinsically connected with other words via stem
include

  * 失う （薄い）
  * 伴う （共）
  * 償う （継ぐ）
  * 担う （荷）
  * 商う （秋）

For years I have been looking up the etymologies of these words individually,
mainly through sites like gogen-allguide.com, but now I believe there should
be a better way to arrange these things. I find 古文辞書s somewhat helpful, but
not right to the point.

旧仮名遣い is not an issue for me so I also welcome suggestions based on it.

### Edit

The above information is not completely correct, especially the part about なう
words. Check the answer(s) before you memorize them. I have subscribed to KDJ
following the suggestion in the answer and it is in indeed helpful.
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question
etymology
How to look up for stems (in the etymological sense)
Your post doesn't actually ask anything. The implied question is _"how shall I
look up etymologies and derivations?"_

Some of the bigger monolingual dictionaries include more etymological
information. I love digging around in derivations, and Shogakukan's 国語大辞典
(KDJ) is a trove of information. I've noticed lately that
[Kotobank](https://kotobank.jp/) includes some content from this dictionary.

Sites like [Gogen Allguide](http://gogen-allguide.com/) can provide helpful
leads. A similar site is [yain.jp](http://yain.jp/), although I don't know
where they pull their information from, so I take them with a grain of salt.
[Nihon Jiten](http://www.nihonjiten.com/) provides etymologies for a limited
subset of entries, most usefully for the names of plants and animals.

After identifying a likely root, I'll often dig around in the KDJ and other
kobun dictionaries to find any likely related terms, and go from there.
Sometimes these other entries might specifically reference the term I started
from, even if that starting entry didn't mention the later terms. Ah, well...

Separately, you also say, _"I believe there should be a better way to arrange
these things."_

I'd agree. Few Japanese dictionaries include information about etymologies and
derivations, and I've had some interesting conversations with native speakers
that lead me to think that many Japanese people don't think much about
derivations. (That's fair; few speakers of any language really ponder these
issues, which is why many of us gravitate to websites like this one. :) )

When I was in my early years of studying Japanese, I was struck by various
seeming similarities and I wanted to know more about the etymologies of
various words, but I was stymied by the lack of such information, even in
reference works. In part to make up for that lack, to make things easier for
future learners, and in part simply to scratch my own itch, I've been
researching terms and adding such information to entries over at the [English
Wiktionary](https://en.wiktionary.org/). I'm sure there are other similar
efforts underway as well.

**Side notes:**

  * 失う is from うし + なう where うし is from ancient verb うす. I think this is more closely related to うしろ (KDJ:「空間的にも時間的にも用い、見えない方をいう」) than to 薄い, since 失う and 後ろ start from the basic idea of "becoming not, becoming invisible", while 薄い is just "thin (but still there)". While 薄くなる is sometimes glossed as "to lose" (such as when said of hair), it really means "to thin out (while still having a presence)". 薄い is probably related to 失う, but I think a bit more distantly.
  * 償う is specifically described in the KDJ as arising from older reading つぐのう, from つくのう, from つく + のう. つく derives from betting term ずく, itself from 尽【つ】く. のう is an alternative form of なう.
  * 商う is much more probably related to 贖【あが】う・購【あが】う, older reading あかう, あかふ, and 贖【あが】なう・購【あが】なう, older reading あかなう, あかなふ. These are clearly あか + iterative / repetitive ふ, and あか + "doing like so" なう.  
The //ak-// root of the あき in あきなう and the あか in あかなう seems elusive. In the
older language, we have both あく（飽く・厭く・倦く） "to become full or satisfied", and
あく（明く・開く・空く） "to become empty or open", which are almost antonyms. How common
are homophonous antonyms in the world's languages? I'm not sure. This has
always struck me as pretty weird.  
By any gates, these two //ak-// roots don't exhibit any obvious connection to
the apparent root //ak-// "to buy, to sell, to barter, to exchange" that we
see in あきなう・あかなう. The best I can come up with is a kind of mashing-together of
the above roots, "to become empty (by giving something away in exchange) and
become full (by getting the other item in the exchange)". That seems ...
unlikely, however.
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