In this quote from Arms and the Man, what is the weapon and why does the speaker object to it? "It is not the weapon of a gentleman."

The weapon is a cloak, and the speaker objects because it does not conform to her romantic ideas about warfare.

Raina Petkoff, a young Bulgarian, makes this statement to a Serbian soldier who has entered her bedchamber.  The soldier is fleeing from a Russian officer, and wants Raina to hide him in her room.  Unsure of Raina's loyalties, the soldier wryly notes that she probably wouldn't want the Russians in her bedroom because she is dressed scantily in a nightdress.  When Raina reaches for a cloak with which to cover herself, he snatches it away, saying,

"No, I'll keep the cloak, and you will take care that nobody comes in and sees you without it.  This is a better weapon than (a) pistol" (Act I).

The soldier reasons that if Raina is not properly dressed, she will be motivated to make sure the Russians do not gain access to her room and thereby find him.  By denying her the cloak, the soldier has found a better weapon by which to gain her cooperation than if he held her at gunpoint.

Raina, who has very romantic and glorified ideas about what a soldier and warfare should be like, is "revolted" by the man's lack of delicacy and chivalry.  She admonishes him that the cloak "is not the weapon of a gentleman", but his keeping it from her is indeed effective in getting her to do what he wants.  He replies, "it's good enough for a man with only you to stand between him and death" (Act 1).