Spinal weapons and similarly high-end stuff is navy-only in the Imperium. Sub-capital grade stuff may be okay, but in that case it's going to come down to how officialdom perceives the need, and for the typical Traveller group that means that a handful of relatively standard turrets are probably okay (especially if the ship has to make regular trips into dangerous areas like the Reach or the Extents), but anything more than that will draw very hard questions and almost certainly a hard no as well.
If they're part of a group where somewhat larger/better-armed ships would be expected, such as a mercenary company, then there'd be a bit more leeway, but it'll still be pretty limited.
Megacorps probably stick to small-to-mid sized ships most of the time since their main interest is economic, and trying to build big stuff is both cost-inefficient and likely to bring navy officials to their door. Nobles might occasionally have a decomissioned naval vessel as a vanity project, but in that case it will be stripped of all naval-grade stuff and essentially function as a high-class liner or the like. Impressive to look at, and certainly nothing that a pirate would want to mess with, but nothing that would compete with proper naval assets.
Outside of the Imperium it'll depend a lot more on local custom and power structures. Organized and law-minded places probably won't be much different than the Imperium is, while in a place like the Extents it's mostly a matter of what you can get away with before the local leadership starts looking at you as a threat.
