There are a few miscellaneous pecularities about the way emotions work that I'm making this article to explain.
The first thing I want to talk about is a few factors besides the magnitude of the trigger that affect the magnitude of emotions:
Temporal distance: The magnitude of a feeling is inversely proportional to the temporal distance from the event that triggered it - that is, they gradually drop off until you fully move on.
Causal distance: The magnitude of a feeling is inversely proportional to the causal distance from the event that triggered it (if applicable). If someone dies across the world, it's bound to affect you much less than someone dying right in front of you, even if both are complete strangers. Worth saying is that this is not only natural and inevitable but morally right.
Sometimes people who don't understand this feel the need to try to correct their feelings, thinking that they're insensitive for not being moved by tragedies across the world. They're not.
One factor that actually isn't its own: probability. It might seem that emotions are stronger when the event that triggers them is less expected. But I think this effect is actually emergent: if you were told something was likely to happen beforehand, you felt the partial-certainty form of the emotion already, and the magnitude likely dropped off, so when the full event comes, it's only changing what you had already accepted as going to happen by half as much.
Limitation: For emotions triggered by external world events, there's either some sort of logarithmic scaling or it's outright capped after a certain point. Maybe both. Because seeing an entire planet get blown up wouldn't cause any kind of severe emotional trauma to most people.
The concept of "caring". Many emotions (self-pity, humbling, loneliness for examples) are inherent to human nature and feeling them is beyond our direct control (though you can still sometimes reason yourself out of them - aka convincing yourself that the trigger isn't as big a deal as you thought). But others (such as sympathy and anger), since their triggers are external world events that we may or may not care about, are actually voluntary - we can choose whether we experience them. This is morally admirable; it is choosing to revere your values over your own happiness. Though exaggerating the magnitude would not count since that would be akin to for example overpunishing someone for a small crime.
The concept of "shadowing". You can experience a diminished form of an emotion through certain means other than its actual trigger. Works of art, in particular, whether stories, music, poetry, or something else, contain bottled emotions that are experienced when the work of art is. That's why art is so powerful and so important to every culture. It's actually what defines art if you ask me.
Curiously, it seems like you can also do it to some extent by simply imagining the trigger. For example, I very often entertain imaginary conversations with real or hypothetical people where I explain what I'm thinking about and they mostly just listen and acknowledge. This is me shadowing companionship.