*al-

The core idea of this root was:

growing, nourishing

It’s the origin of alt and old, and the original sense of those was something like “grown”.

On the Latin side, we have the verb alere, which was also about nourishing, and also the word alto, which had the focus on growing to height .
These Latin words are the origin of:

• adult (“grown up”, at height)
• adolescent (“growing”)
• altitude (“height”)
• alimony (“nourishment”)
• abolish (“grow away from”)
• coalesce, coalition (“grow together”)
• prolific (“growing new fruit”)
• proletarian (in Rome it was the low class, which didn’t pay taxes and only contributed to society by having and bringing up children)

It’s also the origin of world and die Welt.
These words are actually a compound. The first part comes from the Indo-European root *wī-ro-, which meant man and which is the origin of words like virile and virtue.
World and Welt evolved from the idea of something like “the age of man“, in the sense of “the time on this earth” as opposed to the realm of the dead. Over time, it made its way out of this more religious sense and was also used to refer to the planet itself.

German sources also tie in the branch of “alle” here. The underlying logic could be something like “to completion”. But English Etymology.com says the Germanic root *alnaz has no known ancestors.