This is based on opinion. Please don't list it on a work's trope example list.
Tear Jerker / Petite Princess Yucie
Episode 3 has Dan the baker and Mimy's backstories, with him never being around for special moments when she needed him there.
Eoisode 8 has Cocoloo's insecurities over being a ghost, being chosen as a model, and as a Platinum Princess candidate.
Episode 9 has Elmina expressing surprise over Gunbard clapping for Yucie despite mistakes, and that she calls him 'dad'.
Elmina's backstory, with her parents having high expectations, can be enough to bring tears. In episode 12 when she went home to Fluffy Cloud Heaven, she imagines a bunch of disembodied faces laughing at her while she tries to do the dance she couldn't do as a child, causing her to mess up and break down crying, saying "I made...a mistake..."
In episode 18, she flashes back to that same day...but her robot butler picked her up and carried her off, asking her to do the dance just for him. When Elmina protests, saying she messed up, it wasn't perfect, he tells her that he's sure it will be just fine even so.
In episode 12's Heavenly Triathlon, Yucie, Glenda, and Cocoloo manage to inspire Elmina to not give up and that it's ok to try again as they attempt to complete the dance despite mistakes. She eventually joins in and they complete it together.
There's also when the others inspire Elmina to keep pulling at the lever to open Heaven's Gate even when it looks like she can't go anymore. And while Elmina's father still refuses to acknowledge her, she says she can keep trying, and earns the Crystal Flower of Strength.
Episode 13 has Glenda resolving to help Amphi even when it appears he has a lover.
Episode 15 has Yucie in tears after snapping at Pack, and the boy is genuinely hurt. But they make up in the end, bringing happy tears.
In episode 19, Elmina sees the stern, stubborn Mr. Rockwell as being like her father and comes to realize that, like his estranged daughter, she is following a different path than her father is. It culminates in her reading a letter to Rockwell from his daughter Sheena. Sheena says that her only regret is that she never got to see her father smile; Elmina cries afterwards, and writes a letter to the King of Heaven wherein she says that his smile is among her most cherished memories.
Episode 20 has Gunbard and Queen Ercell's backstory. All of it. The two of them loved each other, but could not be wed because Gunbard was her knight and a commoner. He set out to piece together the Eternal Tiara and wish for the ability to marry Ercell; knowing the journey was long and dangerous, she agreed to wait for him. While he was gone Ercell remained faithful and refused any arranged marriages—until her father died. With the people and her servants questioning why she would be so cold as to refuse her father's last wish to marry, Ercell was forced to go through with it. Gunbard finally gathered all the pieces and came home to Ercell and her husband.
Episode 22 has Beth explaining her past and how no one came to help her when she called and cried for help.
The second-last episode, where Yucie's friends give her no choice but to use the Tiara to save Arc, after secretly making a promise that would erase all her memories of them so she could make the wish without guilt. Because making the wish would cause them to cease to exist, and not making the wish would cause the world to be destroyed.
The last episode has Yucie remembering her friends and how they ceased to exist once she made her wish.
It also has The Reveal of Maga Selent, previously shown as a villain, to be the lost princess of the Magic World who Refused The Call and watched her world suffer—when she finally became the Platinum Princess, her friends disappeared pointlessly as the destruction was too much to stop, and every trace of life in the Magic World was destroyed.
The ending theme, "Because I Cannot Say It." Both iterations.
Taken Up to Eleven in episode 25's ending, where the lyrics revert to the pre-episode 14 ending because the other girls were erased.