"Heavy" originates from Old English hefig ("heavy, important, grave, slow"), stemming from Proto-Germanic habigaz ("containing something having weight").  It is closely related to the verb "heave" (to lift) and rooted in the Proto-Indo-European keh₂p- ("to grasp, take, hold"). The term historically implied something difficult to lift or holding substantial weight.   The word was already in use before the 12th century in its modern sense of having great weight.  While primarily referring to weight, it has meant "grave" or "severe" since before the 12th century. 

According to the Oxford English Dictionary (OED), the word heavy (adjective & noun) was first used in English during the Old English period (pre-1150).  The adjective derives from Old English hefiġ (or hefeġ, hæfiġ), which held meanings similar to modern usage, including having weight, important, severe, or oppressive.  The adverbial form is also recorded from the Old English period.  The verb form (meaning to make heavy or burden) is similarly documented from the Old English period.  The OED notes that by the Middle English period, it was commonly written as hevy or heviȝ. 

Emotional heaviness in story writing—often referred to as depth, emotional weight, or "big feelings"—is crucial for creating a lasting impact on readers, transforming a simple plot into a memorable experience.  It acts as the "glue" that binds readers to characters, fostering empathy and ensuring they care about the story's outcome.  

The importance of emotional heaviness in writing: 
Drives Reader Investment and Empath: 
Creating Connection: Readers often turn to fiction to feel something, especially emotions they might avoid in real life. Emotional depth allows them to empathize with the protagonist, turning them into a "compass" that guides the reader through the story. 
High Stakes: If a character's internal world is "light," readers are less likely to care about the external conflict. Emotional weight—fear, grief, or immense joy—makes the story feel important. 
The "Why": While external stakes (e.g., losing a job) provide the plot, emotional stakes (e.g., feeling worthless) explain why it matters. 

Just the facts:

HEAVY Definition & Meaning - Merriam-Webster

HEAVY Synonyms: 701 Similar and Opposite Words | Merriam-Webster Thesaurus

HEAVILY Definition & Meaning - Merriam-Webster