Laden means heavily loaded with something, either physically or emotionally.
From Old English *hladen*, the past participle of *hladan*, meaning to load or heap up. It is related to the word *load* and keeps the older participle form as a separate adjective.
*Laden* is a rare survivor of an older way English formed past participles, like *waxen* or *golden*. When you say “snow-laden branches,” you’re echoing a style of English that has mostly disappeared.
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