The core idea of this root was
swelling, inflating, bulging out
Etymonline.com mentions two separate roots that look identical and have similar meanings, but according to German DWDS.de, there’s one core theme which then grow into two variants.
One branch of the family are words that describe something that’s like a ball or a round swollen thing.
- budget (originally “leather pouch full with coins”)
Another branch is more about blowing air into something to make it swell (or out of a “swelling”).
Then, there’s the branch around the idea of flowers and flora, which is based on the buds bulging in spring.
- blade (originally: the edge of a leaf)
Also blood and bleed tie in here. Just think of the bulging red dot you get when you prick your finger.
And according to the English source I am using (Etymonline.com) also the group around fluid belongs to this family.
However, NOT the group around flow and the German flüssig, which the sources agree come from a root *pleu- which was about flowing.