The tone shifts throughout “The Flea” as the speaker pursues his argument and tries to convince his beloved to take their relationship into a physical realm. Let's take a look at how the speaker expresses and adjusts his tone.
The speaker begins with a calm, rather pedantic tone. He is showing his beloved something he feels is quite important (or at least pretends is important). He logically points out that the flea has bitten both of them, so now their blood is mixed in the flea. There is no shame in that, he argues, so there wouldn't be any shame in having sexual relations either. His argument is faulty, of course, and the poet means it as such, but the speaker at least attempts seriousness.
In the second stanza, the speaker's tone shifts to pleading (or mock pleading in any case). His beloved is on the verge of killing the flea, and he tries to stop her. Notice the exclamation, “Oh stay.” He goes over the top (on purpose) in claiming that in killing the flea, she will be killing both of them, too, for their blood is mingled in the insect. Again, the speaker pretends to be quite serious, but his horror is all staged. He is still trying to persuade his beloved to agree to his overtures.
In the final stanza, the speaker increases his mock horror, for the deed is now done. The flea is dead. The speaker asks some rhetorical questions, trying to convince his beloved of her misdeed. He ends with a quick turn, arguing slyly that her giving into him would have no more significance than the flea's death.