Hundreds of years before a certain pop star pranced around on stage in leather hot-pants and sang "I'm a Slave 4 U," cheesy poets everywhere were saying stuff like "Hey girl—I'm a slave to your love." This idea comes from the courtly love tradition, where male lovers express their devotion by acting like willing servants. In Sonnet 133, Shakespeare gives the convention a shout-out, but then he twists it into something hideous and depressing. When the speaker accuses his mistress of enslaving him and his friend, he's using a metaphor to show how completely powerless the two men feel in the love triangle. He's also accusing his mistress of being degrading and abusive. The overall point? Bad love can feel like bondage, especially when one person has the upper hand and is especially cruel.
Lines 3-4: This is where the speaker says it's bad enough that his mistress "torture[s]" him, but now she's gone and turned his friend into a "slave to slavery," too. Translation: he and his friend are totally whipped. And, in case we didn't get it, the speaker uses repetition—"slave to slavery"—to emphasize his point. Like we said, in the courtly love tradition, dudes are always pretending to be the willing servants of their ladies. But, here, the ugly phrase "slave to slavery" tells us that the speaker and his pal are NOT willing participants in this love triangle and have zero control. So, the phrase "slave to slavery" also has some other possible meanings that you should know about: 1) It could refer to someone who is addicted to a degrading position. (So, maybe our speaker and his friend are both addicted to being with a woman who treats them like garbage?) 2) It could refer to the slave of a person who's got lousy morals and/or has a bad reputation or low social standing. (It's possible the speaker and his friend are acting like "slaves" to a woman who is no better than a lowly slave herself.) 3) It could refer to someone who is forced to do hard labor—as in, the sexual kind. (So, it's possible our speaker is making a reference to his mistress' physical demands in the bedroom.)
Lines 5-6: The speaker doesn't use the words "slave" or "slavery" here, but he does say his mistress has "taken" him from himself and has "engrossed" his friend, too. Given the reference to slavery in the previous lines, the word "taken" can imply that he's been taken, or forced, into servitude. The word "engrossed" means to take possession of, so we get the feeling that the mistress owns the friend like some kind of commodity (a.k.a. a slave).
Lines 13-14: This is where the Speaker says "I [...] perforce am thine." "Perforce" means "of necessity," so he's saying he belongs to her and there's nothing he can do about it. But, did you notice how the term "perforce" has the word "force" in it? It reminds us that the speaker is completely powerless and that his mistress has got the upper hand.