Carrying weight is the "soft" limit. It is unknown if there is a "hard" limit on how heavy a survivor can carry. Each survivor can comfortably carry up to a specific weight (35 lbs for Powerhouse characters, 20 lbs for everyone else). Exceeding this limit will encumber the character.
Encumbered survivors can still move at the same speed, but their stamina drains a lot faster (approximately 3 times faster) when sprinting, making it significantly more difficult to escape from an unwanted confrontation. Also, characters with "Bad back" trait regenerate Stamina 50% slower when encumbered. Backpack weight also counts towards total carrying weight.