Some people try to prove the divinity of the Torah by saying that Hebrew is divine. The divinity of Hebrew supposedly proves that someone (i.e., G-d) has designed it. Apart from the fact that it is quite a leap from the divinity of Hebrew to observing all commandments in the Torah, these linguistic proofs are pretty much nonsense.
One famous example is that ears in Hebrew is אָזְנַיִם (oznaim) and measuring/weighing scales is מְאזֹנָים (me’oznaim). Why would these two words be related? Because the sense of balance which the scales use to measure weight is located in the ear. Which of course G-d would know and take into account when He creates a language.
So how can we explain the relation of these two words without divine intervention? First thing to check is whether this is actually a modern discovery. Since when humans know about the connection of the ear with the sense of balance? If this was common knowledge in the ancient world, there is no argument here. The discovery of the vestibular system is attributed to Pierre Flourens in the 19th century. This does not exclude the possibility that the ancient Israelites knew something and the knowledge was lost, but it is improbable.
Next question we need to address is if the words are really related. Words that have two unrelated meanings but are pronounced the same way are called homonyms. One way this can happen is if two words that were originally pronounced differently change their pronounciations over time and end up being pronounced the same way. A German example is "kiver" (jaw in Middle High German) and "kienforha" (pine tree in Old High German) which have converged to "Kiefer" in modern German (Wikipedia: Entstehen und Verschwinden von Homonymen).
A simple way to test if there might be homonymy going on is to look at the two words in related languages. So let’s check Arabic. Wikipedia gives أذن for ear and ميزان for scales. I don’t read Arabic, so I have no clue how to pronounce this, but the middle letter in ear is clearly a dal (pronounced [ð], like "th" in "that"). The middle letter in scales is a zayin (pronounced [z]). The pronounciation difference in a very related langugae makes it probably that there might have been two different words in Hebrew at one point. Additional evidence is that the pronounciation difference reportedly appears in Ugaritic as well, ‘udn is ear and mznm is scales (Does Hebrew moznayim, scales, derive from Hebrew ozen, ear? citing a mail from Ishinan).
Linguistics is actually a field of research and there is loads of research on the origin of languages and their developments. I am too lazy to go to the university library, but a web search turns up quite some results on consonant shifts between Proto Semitic and Hebrew and also during the development of Hebrew. Here are some references for those interested: Consonants in Semitic languages, Proto-Semitic Phonemes (Consonants) Exhibiting Sound Shifts in Hebrew and their Equivalents in Aramaic and Classical Arabic, Phonetic mergers in the Semitic languages (or if you want a book Aron Dolgopolsky (1999) From Proto-Semitic to Hebrew). All of the references contain a merging of [ð] and [z], so in my opinion the homonym theory is a very plausible one.
But even if you don’t believe in linguistics, and you see the relation between ear and scales as hard evidence for divine design, you are not done yet. To make the argument work, you would need to prove that there is no other language where the two concepts share the same word (I assume Hebrew should be the only divine language). And by prove I mean not just say it, but actually check all languages. Which is quite a task.