Abarim Publications' online Biblical Greek Dictionary
The adverb ασσον (asson) means nearer or closer (Acts 27:13 only), and although relatively rare, in the classics it usually speaks of approaching a specified target. It's the comparative of αγχι (agchi), close or near (unused in the New Testament), and appears to have evolved from αγχιον (agchion) then ανσσον (ansson) then ασσον (asson), says Emile Boisacq (Dictionnaire étymologique de la langue grecque), but doesn't submit why it might have done that. As is, it resembles very few commonly used words in the Greek language, apart perhaps from ασσαριον (assarion), see below, and ασσα (assa), meaning "something" or "some", and the name Ασσυρια (Assuria), Assyria.
There was also a city called Asson, on the west coast of Anatolia, whose name may have come from some pre-Greek language, but which somehow came to be the proverbially nearer port while some other one was the farther one.
The word αγχι (agchi) comes from the Proto-Indo-European root "heng-", to tighten or constrict, hence also English words like angina, anxious and angry. The transmogrification into ασσον (asson), more tightened, remains a mystery.
The noun ασσαριον (assarion) denotes the smallest unit of account and thus the smallest denomination coin in the Grecco-Roman world (whose value tended to fluctuate, but was about a tenth to one-sixteenth of a δηναριον, denarion, denarius, a day's wage). This word transliterates the Latin assarius, which in turn appears to have derived from the noun as, assis, meaning one or unit, which obviously corresponds to εις (heis), meaning one. That means that the word ασσαριον (assarion) essentially denoted the smallest economic unit — comparable with the penny or the cent: the atoms of economy (Matthew 10:29 and Luke 12:6 only).
When Jesus observed that one "one-ling" buys two "thin-lings", he demonstrated that beneath the lowest level of observable monetary reality, the real economy nevertheless continues in a kind of monetary quantum foam: with items of a fluidic nature that in monetary terms are worth less than the smallest financial unit, but which still may add up to that smallest financial unit. Wisdom, of course, works precisely the same way because beneath the level of the smallest confirmable fact (or word or even a single letter) there exists a world of unspoken or unconsidered even unconscious thought, that still may add up to anything from the smallest inkling to a booming flash of light from heaven.
And it gets better yet. An identical word assarius means roasted or dried (over a fire). It derives from the adjective assus, roasted or dried, from the verb areo, to dry (from the Proto-Indo-European root "hehs-", to dry). The obvious pun is that in the Hebrew mind, the world of knowledge and learning is subjected to a similar hydrological cycle as planet earth is. Knowledge drained of uncertainty was considered dry land (see our article on νεφελη, nephele, cloud, for a review of the cognitive hydrological cycle).