The backstory for Athos and Milady De Winter, and the effect their actions (her lying about who she was and then murdering his younger brother, him sentencing her to death by hanging) still have on each other: Athos is still in mourning until he discovers that she's alive, and Milady still harbours feelings for him.
Their feelings for each other are mutual, which is toxic for both of them. Milady even tells Athos that the only way they can ever find peace from each other is if both of them are dead.
D'Artagnan begins the series by losing his father. Then he loses both his father's farm and the woman he loves over the course of one episode.
The woman in question being Constance Bonacieux. And the reason she dumps him is because her husband discovers their love affair and threatens to have D'Artagnan put to death unless she ends it.
Queen Anne and Aramis's conversation after the announcement of her pregnancy. It's all but outright said that Aramis is the father of her child, but he can never be anything other than a bodyguard to the baby. What makes it worse is that Aramis is shown to be very tender towards children, and is hinted to still be grieving over the child he and his would-be fiancee would have had if she hadn't suffered a miscarriage.
The second season premiere gives us the Cardinal giving Aramis a posthumous Kick the Dog by having his subordinate show him Adele's grave, after Aramis had been led to believe that she'd stayed with the Cardinal in the previous season. Adele's grave is in a dank, dark and forgotten place underground, and the epitaph on it? Died For Love. Aramis is utterly devastated, and believes that every woman he's ever truly loved is doomed to die.
Prior to this, Aramis believes that the new Dauphin is his son, and is desperate to be something more than a bodyguard to this child.
Louis mourning the Cardinal's death. It's clear that while he's despairing over the loss of France's most capable minister, he's also grieving the only father figure he's had in his life.
In 2.02, Louis opening up to D'Artagnan while they're captive, about how he lost his father when he was eight. He's almost crying as he expresses his fear that his own son will lose his father young, just like he did.
This moment is a double Tearjerker for being Truth in Television: Louis XIII died when his son was just four years old.
Queen Anne hands-down in 2.03. Her son comes down with a fever, and given the state of medicine back then, it's unlikely that he will survive it. Then she wakes up and finds out that her baby has been kidnapped by someone she trusted (in reality, Constance taking the Dauphin to a public laundry place so the steam can clear his lungs and break his fever), and she has the unpleasant task of telling the King that his heir has been stolen. She goes into his private chambers...and finds him climbing out from his dining table in his underwear, followed by Milady de Winter. The heartbreak and betrayal on her face is palpable.
It's not just Queen Anne who's worried about the Dauphin. Aramis - who may very well be the father of the baby - is devastated by the baby's illness. His worry makes him inattentive during a crucial mission, and that starts a chain of events that ends with civilians and several Spaniards (one of whom was a fugitive who promised King Louis the formula to a special gunpowder that has three times as much combustive power as normal gunpowder) killed, and the fugitive's daughter orphaned and alone.