Roy was found dead in his pickup truck in a store parking lot in Fairhaven in July 2014; Carter, now 20, faces a charge of involuntary manslaughter.
The pair communicated through texts and phone calls, and rarely saw each other in person even though they lived just 55km apart.
In one message before his death, Roy texted Carter that "I keep regretting the past it's getting me upset", her response was: "Take your life?"
In another, she wrote: "Hang yourself, jump off a building, stab yourself idk there's a lot of ways."
As the days got closer to Roy's death, Carter's tone began to change as she seemingly became annoyed that he had not killed himself.
When he offers up reasons not to commit suicide, she appears to encourage him to give in and take his life.
At one point Roy wrote: "Like no I would be happy if they had no guilt about it. Because I have a bad feeling tht this is going to create a lot of depression between my parents/sisters."
She replied: "Everyone will be sad for a while, but they will get over it and move on. They won't be in depression I won't let that happen.
"They know how sad you are and they know that you're doing this to be happy, and I think they will understand and accept it. They'll always carry u in their hearts."
In the final days before his death, Carter repeatedly admonished him for not going through with suicide attempts.
In one message she says: "The time is right and you're ready, you just need to do it! You can't keep living this way.
"You just need to do it like you did last time and not think about it and just do it babe. You can't keep doing this every day."
The prosecution also played two videos found on Roy's computer he had made about a month before his death in which he explained his inner turmoil.
In one, he says he is trying to think positively, watch more films and build his vocabulary to fit in.
However, he says, he is a "minuscule particle on the face of this Earth that's no good, trash, will never be successful, will never have a wife, never have kids, never learn.
"But I have a lot to offer someone. I'm introverted, nice and caring - that's some benefits. I'm a nice kid. But it comes to a point where [I'm] too nice."
In another, he talks more positively about his "social anxiety" and how he has learned not to believe that people are watching him and judging him at all times.
He says he finds it "hard to be in my own skin" but is hoping to stop "weeping and crying over things that are in the past".
"It's going to be hard to accomplish this but I have to, for my own personal growth, accomplish this sense of self-pride."
He adds: "I do have a lot going for me, like I'm a f***ing captain - I just got a job from the Boston Duck Tours to captain their boat - that's a huge accomplishment!"
Sergeant Michael Bates, who reviewed thousands of text messages between Carter and Roy, said under cross-examination that there were also texts in which Carter had tried to help Roy.
The prosecution rested on Thursday after the troopers and the pathologist who conducted the autopsy on Roy's body testified.
The pathologist, state medical examiner Dr Faryl Sandler, said it would have taken up to 20 minutes for Roy to die after the carbon monoxide fumes began entering his truck.
She said it would take 13 minutes for someone to fall unconscious - backing up the prosecution's claim that Carter had plenty of time to persuade Roy to get out of the truck or to alert his family and police.
Sandler also testified that Roy had no alcohol or illicit drugs in his system, just lethal amounts of carbon monoxide and prescription antidepressants.
Under cross-examination by Carter's attorney, however, Sandler acknowledged that she listed suicide as the cause of death on Roy's death certificate.
Carter's lawyer, Joseph Cataldo, says that no crime was committed by his client.
He says Roy had a history of depression, had previously attempted suicide and was entirely responsible for his own death. He says Carter's texts are protected free speech.
The case is being heard without a jury. Cataldo indicated that he planned to make the standard move of asking the judge to grant a not guilty verdict on Friday.
If that motion is rejected, the defence plans to start presenting witnesses.
Where to get help:
• Lifeline: 0800 543 354 (available 24/7)
• Suicide Crisis Helpline: 0508 828 865 (0508 TAUTOKO) (available 24/7)
• Youthline: 0800 376 633
• Kidsline: 0800 543 754 (available 24/7)
• Whatsup: 0800 942 8787 (1pm to 11pm)
• Depression helpline: 0800 111 757 (available 24/7)
• Rainbow Youth: (09) 376 4155
• Samaritans 0800 726 666
• If it is an emergency and you feel like you or someone else is at risk, call 111.