Weedy means thin and feeble — or overgrown with weeds. Two senses that share a plant and nothing else.
The insult is the commoner one in British English, and calling somebody weedy means physically unimpressive, which is unkind and fairly mild. It suits a voice as well as a body, so a weedy little voice is one nobody listens to. The literal sense belongs to gardens and ponds, and a weedy border is one nobody has touched all summer. Both come from weed, which also means a feeble person on its own.
Old English
wēod
Middle English
weed
English
weed
English, today
weedy
From weed + -y. weed comes from Middle English weed, from Old English wēod. From Middle English weed, weod, from Old English wēod (“weed”), from Proto-West Germanic weud (“weed”). Cognate with stq Jood (“weed”), West Frisian wjûd (“weed”), Dutch wied (“unwanted plant, weed”), German Low German Weed (“weed”), Old High German wiota (“fern”). See also woad.
Etymology from Wiktionary, CC BY-SA