Hi Pallas,
Truly a most interesting question about this fascinating period, and I would say extremely complex as it is more something for the historians here.
As for the weapons, I can only surmise that weaponry of these North Italian 'maritime republics' must have been very much similar in the period you describe.
The 'warring city states' of North Italy included others as well such as Milan, Siena, Ferrara, Mantua and Verona, and from what I understand by about the 13th century were typically dependant on mercenary troops in warfare. The 'condotierri' were bands of soldiers essentially from Germany and Switzerland , and it would seem that their arms were certainly well diffused into the scope of weaponry used in these city states.
With the Maritime Republics you are focused on, since these were key to the vast trade networks of the times, naturally influences from the East must have brought in Byzantine and Arab forms along with others.
The diffusion and development of weaponry is clearly a challenge without really being somewhat specific as to which type, period and region and developing patterns in the variations against historical resources. This is pretty much what you're trying to do here of course.
One of the best references for Italian weapons of the Renaissance as far as swords, daggers and some polearms is "Armi Bianchi Italiene" by Boccia & Coelho. While its period essentially opens at the terminus of the end of your 15th century scope, it does show the weapon styles of these city states with similiarities and some subtle differences.
As for the earlier period from 900AD onward, I would suspect that searching the works done by Dr. David Nicolle would be an excellent start. I think even some of the Osprey titles may offer some insight, I believe there is one on Venice for example. Nicolle did a two volume set on weapons of the Crusades that had a lot of weaponry that may be pertinant.
Dalmatia seems to have always been key in providing forces to these Italian city states, with of course the most familiar being those who became the guards for the Doge of Venice. The development of the schiavona swords would be a good example of infusion from European/Balkan sources, although clearly later.
The subject of Genoa and its Black Sea colonies is a great topic that is key to much of our study on the influences of Italian weapons and trade that entered many regions through these ports. I look forward to hearing of good titles on this as well. It seems there was a book titled 'the Black Sea' but I cant recall details offhand.
I thought I would just open this up with what little I know of this history to suggest some possible avenues for research, and look forward to input from our far better versed historians out there.
Great topic and thanks for posting it Pallas !
All best regards,
Jim