However, in the case of the pound, it is not clear what it originally was equivalent to.
I think you're going to find that there is no known meaningful answer to this question, just a deep rabbit hole going back to the origins of civilization and written history, and quite possibly beyond.
The best we can say is that the various historical weight/mass measures known by the name of "pound" (or "Pfund" or "livre" or "libra" or whatever the equivalent local name happens to be) were defined in terms of physical reference weights (i.e. typically blocks of metal stored in a vault somewhere) — exactly like the kilogram was defined until very recently (from 1799 to 2019).
Historically, these reference pounds were established by local rulers and merchant organizations, and their weight was based on that of other, earlier pound weights used in the same or nearby regions, sometimes with deliberate adjustments up or down as per the whim of those in charge of setting up the local standard.
Wikipedia has a nice scan from an old German textbook from 1848, listing various local pounds and other weights and their ratios to each other. I'm not going to transcribe the entire table here, but the key take-home message here is that, even among the listed units with names clearly cognate to "pound" or "libra", the weight varies from 763 g (Milanese Libbra peso grosso à 12 once) down to 317 g (Genoan Libbra peso sottile; even the Genoan Libbra peso grosso is only 349 g!), i.e. by a factor of over 2.5.
(The list, written half a century after the introduction of the metric system, also includes several local pound weights of exactly 500 g, which falls comfortably within the typical "pound" range, as well as at least one Libbra metrica that is actually a synonym for the kilogram.)
Thus, in tracing the origin of the various pound weights, it's clearly not reasonable to expect the actual weight to have remained particularly closely fixed. The best we can hope for is something in approximately the right ballpark with, hopefully, an attested historical or etymological connection.
That said, most of the pound weights used in Europe clearly trace their name and approximate mass to the ancient Roman lībra pondō. The Roman libra wasn't a perfectly constant measure, either, nor is its mass perfectly known: Wikipedia lists an average consensus weight of 328.9 g, but notes that various modern estimates have ranged from 322 g to 329 g.
(The name of the unit itself is fairly transparent in Latin: lībra, in addition to "pound", means "scales" or "balance". As for pondō, the origin of the English word "pound", it simply means "by weight".)
As for where the weight of the Roman libra came from, that I know less about, but I can at least make some semi-educated guesses. As the Wikipedia article linked above notes, the Roman units of measurement were in large part based on the Greek system of measures in common use in the Mediterranean at the time. Thus, it seems plausible that the Roman libra was ultimately based on some version of the comparably sized Greek weight unit μνᾶ (mina).
The μνᾶ also came in several different regional variants: Wikipedia gives reconstructed weights of 341 g for the Attic/Euboean mina and 630 g for the Aeginetic mina, again showing the great variation between homonymous units from nearby regions. In light of this variation, it seems perfectly plausible to me that the Roman libra might've originated from the Attic mina or some local variation of it.
As for the Greek mina, just the name alone clearly links it to the ancient Mesopotamian mina (Sumerian 𒈠𒈾 = ma-na, Akkadian manû, likely from an Akkadian verb meaning "to count").
This is the one part of the story for which I can actually cite a somewhat more authoritative source than Wikipedia, namely the rather extensive entry on "measures and weights" (indexed as Maße und Gewichte in German) by M.A. Powell in Reallexikon der Assyriologie vol. 7, pp. 457–517.
As Powell notes, the name mina (or, rather, 𒈠𒈾) as a unit of measurement is attested from the Early Dynastic Period (3rd millennium BCE) onwards, although the unit itself — defined as 1/60 of a talent (Sumerian 𒄘 = gun2, Akkadian biltu, literally "burden" or "load") — may be older, possibly even prehistorical.
The typical Mesopotamian mina weighed about 0.5 kg, although in the Neo-Assyrian period (c. 9th to 7th centuries BCE) a "heavy mina" of twice the weight, or about 1 kg, apparently emerged alongside the traditional "light mina". To quote Powell (RlA 7, p. 509):
"Most weight specimens incorporate mina norms that fall in the range of 500 ± 40 g. Within these bounds a plethora of actually used norms existed (sometimes this is explicitly noted in texts), but most of these norms cluster in the range 480–510 g. […] As conventional values, mina ≈ 500 g., shekel ≈ 8.333 [g.], recommend themselves. More specific values (which certainly existed in abundance) require substantiation by monumental and textual evidence with proper attention to the specific historical situation."
The fact that, after millennia of semi-random drift and tweaking and re-standardization, these ancient mina weights should come to so closely coincide with the modern "metric pound" of 500 g (and the Assyrian "heavy mina" with the kilogram) is surely a pure coincidence, but an intriguing one.
So where did these ancient Mesopotamian weight measures come from, then? Honestly, there's a fair chance that we'll never know, since their origin may well be buried in prehistory.
It's quite possible that they simply come from yet older standard reference weights, perhaps originally chosen as standardized approximations to loose everyday measures like "the load of grain a man can comfortably carry" and simple fractions thereof.
That is not to say that they couldn't have been defined in terms of some (more or less) natural references. Indeed, the Mesopotamian mina was defined to equal 60 shekels (Sumerian 𒂆 = gin2, Akkadian šiqlu), and a shekel as 180 "grains" or "barleycorns" (Sumerian 𒊺 = še, Akkadian uṭṭetu, both meaning "grain" or "barley"), whose weight of approx. 45 mg is a reasonable approximation to that of typical actual barleycorns. (The Greek mina was similarly divided into 100 drachmas, each drachma into 6 obols, and each obol into 12 barleycorns.) But, at least if Powell's summary is to be trusted, this seems to have been an artificial retrofit — the original base unit seems to have been the "burden" / talent of approximately 30 kg.
Also, as the traditional Sumerian measure systems were reformed and standardized in the Akkadian period (late 3rd millennium BCE), the weight, volume and length measures seem to have been linked such that one sila (≈ 1 liter) of water would weigh 2 mina and fill a cube with a side length of 6 fingers (≈ 10 cm). (The parallels to the later development of the metric system about 4000 years later are again striking, though surely coincidental!)
In some sense this is a very natural way to link weight and volume measures, if one wishes to do so, as (fresh) water is one of the few substances readily available to a bronze-age society with a more or less fixed and consistent density. But again this linkage seems to have been a retrofit to an existing system, and while the volume measurements in particular were significantly revised in the Akkadian reform, the Akkadian "royal mina" does not seem to have differed much from the various pre-reform mina weights in use at the time.