Power is a big topic in Major Barbara, and weapons and arms are (unsurprisingly) a big symbol of it. There's a lot of talk about the best way to get power, and what kind should be pursued—is physical dominance the most important? Governmental? Spiritual? Lady Brit just seems to want her family listen to her, whereas Barbara wants the power to save souls. Meanwhile, Barbara's fiancé, Dolly, ends up saying he wants to equip the common man against their tyrannical overlords—sounds…not easy.
Several of the characters end up believing that Undershaft's weapons factory will help them attain the kind of power they desire. Relax, they're not planning to take up Undershaft's arms and lead an armed rebellion; they just believe that working with Undershaft and/or his employees will give them the power they need to create changes in their personal areas of interest.
Take Barbara, for instance. Even though she abhors violence and murder, she nevertheless comes to believe that being involved with her father's factory will expand her evangelizing powers, giving her access to a whole new set of converts who would come to the faith from a place of comfort and security, rather than desperation. Put a bit differently, her converts will come to the table from a more empowered place, which means they will come to the faith for the right reasons rather than just because they are hungry or cold.
Meanwhile, Dolly believes that working for the Undershaft company will allow him to "make power for the world" (404-405). Although Dolly maintains that all power is ultimately "spiritual," he also believes that that kind of mojo is hard to convert into action without the proper opportunities or tools:
I think all power is spiritual: these cannons will not go off by themselves. I have tried to make spiritual power by teaching Greek. But the world can never be really touched by a dead language and a dead civilization. The people must have power; and the people cannot have Greek. Now the power that is made here can be wielded by all men. (3.407)
When Barbara suggests that he is simply describing the power to blow innocent people up, Dolly objects, saying that he's merely giving the good the best possible chance of defending themselves against the bad:
You cannot have power for good without having power for evil too. Even mother's milk nourishes murderers as well as heroes. This power which only tears men's bodies to pieces has never been so horribly abused as the intellectual power, the imaginative power, the poetic, religious power that can enslave men's souls. As a teacher of Greek I gave the intellectual man weapons against the common man. I now want to give the common man weapons against the intellectual man. I love the common people. I want to arm them against the lawyers, the doctors, the priests, the literary men, the professors, the artists, and the politicians, who, once in authority, are more disastrous and tyrannical than all the fools, rascals, and impostors. I want a power simple enough for common men to use, yet strong enough to force the intellectual oligarchy to use its genius for the general good or else perish. (408-409)
So there you have it: For Dolly (and ultimately Undershaft and his daughter), weapons represent power—and empowerment. It's a controversial view, sure, but Undershaft has the family pretty much convinced by the end of the play.