Before expand meant 'to grow bigger', it meant to physically unfold. Latin expandere — from ex- ('out') and pandere ('to spread') — described the act of opening out a rolled scroll or unfolding a piece of cloth. Growth was not the point; opening was.
The Latin pandere, from Proto-Indo-European *peth₂- ('to spread'), produced a scattered but connected family in English. Pace comes from Latin passus, the spread of the legs in a single step. Patent descends from Latin patēns, 'lying open' — a patented invention is one laid open to public knowledge in exchange for legal protection. Compass originally meant 'step together', from com- + passus.
The Greek branch of the same root gave English petal, from petalon — 'a leaf spread out'. A flower opening is, etymologically, the same action as a scroll unrolling.
The abstract sense — an expanding economy, an expanding universe — developed gradually from the 16th century onward. It carries a spatial metaphor: growth is imagined as something unfolding outward from a centre.
The expanse — a wide, unfolding stretch of landscape or sky — preserves the physical image most vividly. An expanse of water is not merely large; it is spread before you.