Well, the rulebook does not say exactly (aggravating when it does that), but from where it talks about favored weapons and the note with the cost for adding them to a standard kit, it appears that adding a favored weapon to a list does indeed cost points.
Of course, with the vagueness of the rulebook on the subject, and the lack of conformation (That I could find) on the internets, if you can find something that is somewhat official looking and says otherwise, well, that will reverse the ruling. But until then, you get the choice of a heavybolter or missiles. Sorry.
Class descriptions, sidebar, specialist equipment section: "Common Craftmanship Missile Launcher with 5 frag missiles
or common craftsmanship heavy stubber
or Common Craftsmanship Regimental Favored Heavy Weapon
Regiment Creation, Regiment Creation Rules, Favoured Weapons: "Each Regiment may choose one Basic and one Heavy Weapon to be their Favoured Weapons, these weapons must be Very Rare or more available. Members of the Regiment get +10 on logistics tests to obtain these weapons and their ammo."
Nowhere here does the game mention having to pay a points cost to gain these, but for in the Additional Equipment Section, table 2-6, where adding a favoured weapon to the kit can be done for 10 or 15 points. Considering precedent with additional equipment and standard equipment dictates that each member of the squad is issued the full list, and that the heavy need not have the regiment pay points for any of the other non-favored choices, nor is there a particular provision in the Favoured Equipment paragraph to enumerate such, and additionally that there is a provision in the Favoured Weapons tab which enumerates that weapons above Very Rare cannot be selected, so as to prevent taking them using this specialist equipment method, it is clear that the regimental favoured weapon can be taken as specialist equipment.
Further, assuming that the first quote merely refers to the taking of a single squad-wide favored weapon, namely the one in table 2-6, there would be no point in opting for this point rather than taking a missile launcher or somesuch in addition to the weapon one would be issued anyway, and if one interpreted the table as not being applied to each squad member, it would be impossible to, say, give everyone laspistol sidearms, because one can only take the upgrade once, meaning one pistol, while with an interpretation based on the table being one upgrade applied to all members, this upgrade and the rest function as intended, while preventing one from carrying several pistols each for such shenanigans as dual wielding pistols on the cheap or arming large militia forces using spare pistols.
EDIT: Further, if favoured weapons required purchasing on a per-member basis, the standard regiments would include points allowances or something so you could buy the favoured weapon for your heavies and specialists. They don't.