There are a couple answers to your inquiry, which I will try my best to detail below...basically though, arms and armor were largely manufactured by local smiths in individual cities...there were not, as far as I know, large manufacturing centers, but rather each smaller city produced what was needed to maintain their own armies. Rome also produced their own weapons and armor, but requested arms and armor from the allies when the need arose. Scipio, for example, when preparing for his excursion into Africa, made great use of allied assistance. Livy states "... Although Scipio had not obtained, nor earnestly solicited, authority to levy [83] soldiers, he yet was permitted to enrol volunteers; and as he had declared that the fleet should be no expense to the public, so he might receive such contributions as should be offered by the allies for building new ships. The states of Etruria first promised to give assistance to the consul, proportioned to the respective abilities of each; the people of Cære engaged to bring corn, and provisions of all kinds, for the seamen; the Populonians, iron; the Tarquinians, canvass for sails; the Volaterrans, tackling and corn; the Arretians, thirty thousand shields, the same number of helmets; of javelins, short pikes, and long spears, each an equal number, amounting in the whole to fifty thousand; to supply axes, mattocks, bills, buckets, and millstones, sufficient for forty ships of war, with one hundred and twenty thousand pecks of wheat; they also promised to contribute to the expense of the decurions* and rowers. The people of Perusium, Clusium, and Rusella gave assurance of fir for building ships, and a large quantity of corn. The states of Umbria, with the people of Nursia, Reate, and Amiternum, and the whole country of the Sabines, engaged to furnish soldiers. Fir, however, he took out of the woods belonging to the state. Great numbers of the Marsians, Pelignians, and Marrusinians, voluntarily gave in their names to serve in the fleet. The Cameritans, though confederated with the Romans on equal terms, sent a cohort of six hundred men and arms. Having laid the keels of thirty ships, twenty quinqueremes, and ten quadriremes, Scipio pressed forward the work by his personal attendance, in such a manner, that on the forty-fifth day after the timber had been brought from the woods, the ships were rigged, armed, and launched." Rome also, after taking a town or city, gained arms and armor from the conquered town, either from plunder or from forcing the town to give up their arms as a condition of being taken under the Roman wing. Less commonly, arms were taken from slain enemies. Most often these were put into temples in the various cities as gifts to the gods, but there are records of the temples being plundered and their arms taken and put to use under extreme circumstances. I hope this answers your question...sorry for any formatting errors...I'm on mobile so it's not easy to type something this long!