The Philistines had disarmed the Israelites to prevent rebellion.
Gill's Exposition on 1 Sam. 13:19,
"Now there was no smith found throughout all the land of Israel,.... The Philistines, when they ruled over them, having removed them into their own country, and forbid any to learn or exercise that trade in Israel:
for the Philistines said, lest the Hebrews make swords or spears: this they did to prevent their having arms, and the use of them, that they might not rebel against them, and fight with them, and overcome them; it was a piece of policy to keep them subject to them; so Nebuchadnezzar, when he conquered the Jews and carried them captive, took care particularly to carry away their smiths, and left none but the poorest sort of people in the land, 2 Kings 24:14 and Porsena, king of the Etrusci, when he made a covenant with the Romans, upon the expulsion of their kings, made this a condition of peace with them, that they should use no iron but in husbandry (h). When this course was taken by the Philistines with the Israelites, and how long it had continued is not certain; it is probable it might be in the space of forty years they ruled over Israel, in which Samson was born, for we never read of any sword or spear that he made use of; and though there were two battles in the times of Eli, in both which Israel were beaten, they might make use only of bows and arrows, slings, and stones, clubs, &c, as also in the battle of Saul with the Ammonites; and as for the defeat of the Philistines in the time of Samuel, it was by thunder; and though the Philistines were then subdued, yet, as Samuel grew old, they regained their power in a good measure, and the Israelites had not spirit enough to oppose them, nor diligence and industry to learn and revive the trade of smiths among them; not even for what was necessary to husbandry, as the following verse shows.
(h) Plin. Nat. Hist. l. 34. c. 14. " Source: here
A shekel was a weight. There are three different shekels mentioned in scripture: silver shekels of Gen. 23:16 ; the shekel of the sanctuary in Ex. 30:13, which was 20 gerahs; and shekels measured by the king's weight in 2 Sam 14:26. These may have varied. An article discussing weights and measures can be found here.
Another source identifies the gerah as being 1/50th of an ounce, or 0.6 grams. Then, the sanctuary shekel would have been 0.4 ounces, or 12 grams. See here.
But, 1 Sam. 13:21 is not translated the same in the English versions.
Verse 21 In Young's reads:
"and there hath been the file for mattocks, and for coulters, and for three-pronged rakes, and for the axes, and to set up the goads."
The KJV reads:
" Yet they had a file for the mattocks, and for the coulters, and for the forks, and for the axes, and to sharpen the goads."
Excerpt from Gill's Exposition on vs. 21:
"(The word for "file" in the verse is "pim", and occurs only here in the Hebrew scriptures. It is not used elsewhere in other Hebrew writings. Therefore the translators of the 1611 Authorised Version had only the root derivation to deduce what the word meant. Literally, it means "a file with mouths". However, recently archaeologists have found a stone inscribed with this word. Also they found a stone inscribed with the word "shekel". Hence they deduced that the word was really a weight of measure equal to about one third of a shekel. Newer translations usually translate this as "the charge was a third of a shekel ...", hence removing the obvious contradiction between this verse and the preceding one. Editor.) " Source: here
Ellicott's Commentary offers:
"The LXX. read this 21st verse with considerable changes: “And the vintage was ready to be gathered, and the tools were three shekels to the tooth to sharpen], and to the axe and to the scythe there was the same rate” (or, as the Greek has been rendered,” tools cost three shekels apiece [to sharpen]”)." Same source as above.
There appears to be differences in the amount the Philistines charged. But, Interlinear has it as "a shekel" for all of the tools.