This is based on opinion. Please don't list it on a work's trope example list.
Tear Jerker / Mario & Luigi: Partners in Time
When a character faints. When an Adult faints, their younger version drags them to safety, and if one of the Babies, the other starts to cry and then carries the other for the rest of the duration of the battle! It brings tears to your eyes.
None of the bosses which are obviously sapient show any hesitation in attacking Mario and Luigi while they are carrying their baby selves on their backs. Not to mention that killing their baby selves would affect other characters more than just emotionally. This becomes despicable and heart-wrenching for the player when the adults faint and cannot continue battling, prompting their baby selves to drag them away to safety and you are left...fighting the ruler of an entire race of aliens...as toddlers. To make it even worse, once one of the babies faints the one that's still standing will cry out the name of his fallen brother in grief, run over to him, and attempt to continue to survive enemy attacks while carrying his unconscious brother on his back, noticeably strained by the weight. To make matters worse, it makes it much harder to dodge enemy attacks, making it all the more likely for you to fail in doing so and letting the last brother awake get KOed.
When Toadbert, Toadiko, and Kylie turn into Shroob Mushrooms.
The whole section at Hollijolli Village. The music is a very eerie rendition of Jingle Bells, and it's a town that got destroyed by Shroobs while they were celebrating Christmas. And they're harvesting the souls of the towns people for UFO fuel. On Christmas.
It's made worse by the fact that this is the very first level of the game, and thus the first impression you get of the Shroobs. They destroyed it on Christmas. Being the first level and all, you'll feel quite helpless to see the remains of a destroyed town. On Christmas.