IMTU, off the cuff -
Imperium
"Defensive" weaponry is allowed on commercial ships - but since every megacredit counts, and even the turrets need maintenance, anything operating more than 10 parsecs from the border is generally unarmed. Spinal weapons and nuclear payloads are banned outright for commercial ship designs.
Extra-Imperial traders must have their ships modified to comply with these regulations, and registered -before- entry into the Imperium. Failure to do so will be seen as an attempt to 'smuggle' said weapons into Imperial space at best, and as an act of piracy or even war at worst. Cooperation in these cases will result in impounding of the vessel until such a time as the MoJ is satisfied with ship refitting, licensing, and fines and/or prison sentences of the guilty party having been resolved.
Solomani
Depending on the internal substate of the Confederation, any number of rules may be locally in place, but for the most part the 'cold war' nature of its relations with just about every major interstellar power, especially the Imperium, means that most merchanters go fully armed pretty much anywhere within 30 parsecs of a Confederation border.
Any ship owned/operated by a member of the Home Guard is pretty much expected to have their ship armed and available for auxiliary service 'just in case'. The heads of SolSec aren't too happy about this, but have accepted it as the status quo.
For the most part, the same bans against nuclear weapons and spinal mounts are pretty much the same as in the Imperium, with the exception of The New Slavic Solidarity state in Magyar sector, who's internal laws require merchants to be allowed nuclear payloads for defensive purposes. These laws date back to the Long Night and the continuation of which were part of the conditions of joining with the rest of the Confederation at its inception. SolSec is extremely unhappy about this, but a subclause to their joining precludes Confederation interference on this issue and makes secession a legal option if future regulations don't include this exception.
Vargr
YMMV as usual. Some states are just large enough to control some of what goes in and out of their core systems, and their border system defenses will react according to their internal laws and relative stability of whatever central government is in control at the time.
Society of Equals for example, has much the same restrictions as the Imperium. The Anti-Rukh Coalition oddly has a rule restricting defensive weaponry to offensive weapons only - ie. sandcasters aren't allowed. If you fill a turret, it must be with something offensive.
Hiver
"There are no restictions as such, but why would a peaceful ship want to arm itself anyway? All right, very well, if you insist. Oh, but I'm sorry, it appears the closest manufacturer of nuclear warheads compatible with your ship is backlogged supplying the Federation Navy for the next seven months I'm afraid. The next closest is *checks readouts* Dwelve, twenty-five parsecs away and requires refitting at site. That particular nest also requires you fill out their extensive customer satisfaction surveys, future reload exclusivity contract (their refitting of your weapon systems will require this anyways), and come in once every year for an ordinance check - they'll replace any warheads still under their rather generous warranty for free.
"Oh, and don't worry, the situational lockouts are quite generous in permitting your ship to defend itself with the ordinance in case of a pirate attack - the system is really quite smart and exceedingly hard to feed false data to, and any tampering will disable the system until a full investigation at Dwelve can clear the customer of any misuse of the system and reactivate it."
"Oh, you'll just take standard High Explosive ordinance? Very good, sign here and here, and our technicians will meet you at your airlock within the hour. I promise, you won't be disappointed!"
Foreven, The Beyond, Far Frontiers, Vanguard Reaches
Anything outside the Imperial client states and the Consulate(s) and other established interstellar states is pretty much wild wild west, but few besides pirates actually arm with nuclear ordinance simply for the fact that its expensive, and eventually they'll have to cross back into these larger states to do business. A few free traders and even multi-ship companies will have wilderness hideyholes one jump outside the major powers' space where they can re-arm with nuclear warheads for long traderuns into the wild.
Some independent systems look the other way simply because without these heavily armed merchants, they might not see traffic come through for weeks, months, or even years at a time. Other systems can't even enforce their will against ships with standard ship lasers and HE missiles due to lack of technology, population, wealth or sometimes all three.