The Big Emotional Episode is a story of some other kind that happens to hit one of the PCs where it hurts emotionally. This is the sort of thing that should definitely be discussed with the player beforehand, as some players aren't keen on putting their characters through the wringer.
Father’s Day is a Big Emotional time paradox story, unique to time travel series where rather than just having painful memories you can get in a time machine and visit them. It asks the obvious question “what would you change if you could go back in time?” and along with dangerous paradoxes, Reapers and the TARDIS turning into an ordinary police box, its main drive is the Big Emotional stuff.
The Girl In The Fireplace is a Big Emotional Episode more than it is a Celebrity Historical, as well as a timey-wimey format-bender. Here, the Doctor’s feelings - and Reinette’s, and Rose’s, and Mickey’s - are an added level turning a time-jumping adventure story into a sweet, sad romance.
Doomsday is a Big Emotional Season Finale. So is Journey’s End. So is The End Of Time. Season Finales tend to be Big Emotional Episode because characters leave, die, change drastically, get stuck in parallel worlds, and don’t always get a proper chance to say goodbye. The departures are foreshadowed and threatened in advance, but still shocking.
Human Nature is a Big Emotional Format-Bending Historical Secret Invasion Two-Parter. The historical setting informs the emotions, the format-bending allows them to happen and the secret invasion builds them to breaking point.
Turn Left is a Big Emotional Doctor-Lite Format-Bending Aliens Of London episode. It’s a classic parallel world, played as grim as the show goes since its revival.
The Sarah Jane Adventures tends to give its Big Emotional Episodes to the Trickster, as he manipulates Sarah Jane’s feelings to catch her off guard.
As you can see, there’s only one or two full-on weepies per series, because there’s only so much Big Emotion anyone can take. And that’s important to note, because some players will not want to bring this to the table, and others won’t necessarily want it in a given session.
Example: The Step
(An Aliens Of London Big Emotional Episode. These should always be tailored to individual PCs, but this is an example of a phenomenon that could lead to Big Emotion.)
Stepping out of the TARDIS, one of the travellers sees, or thinks he sees, someone he loved and lost years ago.
In truth, this is a psychic lure to lead a time traveller away to a stranded alien who communicates by accessing memories. So it explains that its ship is damaged by dropping the traveller into a memory if the TARDIS needing repaired... and that it misses its loved ones by throwing him into memories of those he has loved and lost.