to stretch out or spread something: to extend a hand, arm, or fabric into open space
This is the plain physical core of the word: to take something and reach or spread it out so it covers ground or fills space. A hand or a staff is thrust forward, a measuring line is run out, a tent cloth is pulled taut over its poles.
From this everyday picture the Bible builds two of its grandest images. God spreads out the sky the way a person pitches a tent, unrolling it like a curtain over the earth. And God's saving power is pictured as an arm reached out at full length, the famous outstretched arm that rescued Israel from Egypt. In every case the action is the same: something is extended outward from its source into the open.
The sense covers both the act of stretching and the resulting stretched-out state, which is why the word can describe a tent already pitched or heavens already spread as easily as the act of pitching or spreading them.