'Deep' has meant depth for millennia — from PIE *dhewb- (hollow). All abstract 'depth' is metaphor from this.
Extending far down from the top or surface; extending far in from the outer edge; very intense or extreme; profound.
From Old English 'dēop,' from Proto-Germanic *deupaz, from PIE *dʰewb- meaning 'deep, hollow.' The same root may be connected to PIE *dʰewb-/*dʰub- meaning 'to sink, to be hollow,' though this is debated. The word has maintained its spatial meaning with remarkable stability for over a thousand years while also developing rich metaphorical extensions — deep thought, deep feeling
The common expression 'deep-seated' is frequently misspelled as 'deep-seeded,' but the original metaphor is spatial, not agricultural — something deep-seated is lodged deep in a seat or position, not planted deep like a seed. Old English 'dēop' could also mean 'mysterious' and 'awful,' senses that survive in phrases like 'deep secret' and 'in deep trouble.'