[Randallw]

Weapon mounts availability differ on whether it is Stock, or a Mod. Within the Stock game mounts are dependant on ship size. Until you reach a certain size you are restricted to a normal mount. When you get large sized vessels (cruisers or so, but I'm not sure exactly which size) you can have large mounts. When you reach huge ships (like Battleships, again not certain) you get huge mounts. As a result the benefits of large vessels is not just that you can equip them with more but that they carry weapons that have longer range and greater damage. Bases, mainly because they dwarf "ships" have large mounts that increase range and damage. The advantage of larger weapons platforms is that they each allow a larger wepaons mount. So a large weapons platform is 3 times the size of a small one but can have huge weapons mounts. The same applies to satellites.
Within Mods it is possible to get mounts by researching tech. One mod (devnull possibly?) allows enhanced range, or spinal mounts etc.

Edit: when I wish to find what mounts will be available on a future ship in development I start a game with maximum tech. Design ships by choosing the ship size, then pick a weapon (taking into account beam weapon or missile), you can look to see what mounts are available with the ship in question.

edit: Followed my own advice for stock game

Ships (ship mounts do not grant extra range)
Mount Dmg minimum size
large x2 400kt
hvy x3 800kt
massive x5 1200kt

Bases
large x3 (+2 range) 500kt
hvy x5 (+4 range) 1500kt
massive x7 (+6 range) 2500kt