The core idea of this root was:

two

And there are basically four big branches we can identify. The first one is duo, and here the sense of two is pretty obvious.

• duet
• dual
• double
• doubt (“on two sides)”
• dubious (“two faced”)
• duplicity (“two faced”)
• …

The next branch is around the syllables: di-, dia-. In some words in this branch the idea of two is pretty clear. Others  are about a theme of through which is probably an extension of the idea of from one side to the other.

• carbon dioxide (“carbon with two oxygen”)
• diploma (originally “official paper folded twice”)
• diabetes (“passing through”, referred to excessive peeing)
• diarrhea (“flowing through”, referred to.. well… you know)
• diagram (“marked/bordered by lines”)

The third branch is bi-.
Here, the theme of two is also very strong, but sometimes it’s fairly obscured.

• binary
• binocular (“two eyes”)
• biscuit (“cooked twice”)
• combine (“make two, put together”)
• balance (originally “scale with two pans”)

Last but not least, we have the Germanic branch of two, twi-  and zw(e)i.
Besides the actual numbers, this branch has a quite a few words that are about coming from two sides.

• two, zwei, twelve, zwölf, twenty, zwanzig
• twilight (“double light”)
• between (“by/within two”)
• twine, twist (probably originally about “twisting two threads together for a rope”)
• twig, Zweig (branch splitting up “two ways”)
• Zweifel (“on two sides”)
• zwicken (to pinch – “pinch between two”)
• zwingen, Zwang (to force – “pinch between two”)

The connection of “Zweck” was an assumption in etymological sources for a while, but it’s not supported by newer research. Still, I decided to include it here.