First, deport showed up in the late fifteenth century meaning…to behave. I can’t even wrap my head around that. The other deport, like you would a person, didn’t show up until the mid seventeenth century! And they actually have slightly different origins. That weird deport comes from the Old French deporter, which could mean behave or things like be patient, amuse, delay, treat kindly, and take sexual pleasure with. Seriously, what the hell. Like the other -port words it comes from the classical Latin portare, carry, and the de- prefix means from or off. No, that makes no sense. It makes less than no sense. The other deport—the one we still use—came to us from Modern French, where it was déporter, carry off (or, you know, deport), and before that the classical Latin deportare, transport. Now I want to take the other deport and yell at it, “See?! This is how an etymology is supposed to go!!”
Ahem. Speaking of transport, it showed up in the late fourteenth century coming from the Old French transporter and classical Latin transportare, which is just transport. The trans- part means across, so it’s carry across. It’s nice to read something that doesn’t make me want to scramble my brains with an ice pick. Deport. PS., teleport didn’t show up until 1940 and is actually tele- (far off) plus transport. I’m assuming sci-fi has something to do with that.
Support showed up in the late fourteenth century from the Old French supporter and classical Latin (I’m sure you can guess it) supportare, or support. Support’s original definition was things like hold up or sustain, and it’s a mix of the prefix sub-, up from under, and portare, carry. So it’s to carry up from under, which makes sense. I think.
Finally today, we’re going to do some quick etymologies of the final port words. Passport is from the sixteenth century, coming from the Middle French passeport, authorization to pass through a port. It’s literally pass + the ship port. Next, purport showed up in the early fifteenth century from the Anglo French purport and Old French porport/purporter, contents, or convey. That’s a combination of pur-, which is basically por- or pro- and means forth, and porter, which of course comes from portare. Purport is to carry forth. Lastly there’s comport, which showed up in the late fourteenth century from the Old French comporter, endure or behave. It’s from the Latin comportare, which could mean things like transport or bring together. That last one makes sense since com- means together, so it’s carry together. Not that we use comport much these days…
TL;DR: If you ever want to etymologize the word port for your blog, it’s going to take way longer than you think.