Have I been pampering a weed?

I'd try uploading to google image and see if it puts you on the right path.

First guess is a pine tree. Are the branches brown (hard to tell in photo)? Have a look here, click the Jeffery Pine image to scroll over it.

Looks like a pine. You do know Jeffrey Pines are a little slow off the line? Assuming everything goes okay you might have a 5' high tree in 10 years or so. The good news is the oldest one on record is over 600 years old. Unless you're planting for the generations you might want to think about an Eastern White Pine.

I'm not an arborist and this is a completely unscientific opinion, but my general idea is the western pines evolved in a semi-arid environment and have sort of a wait and see approach to growth.

I have a bed where a bush died, from cedar apple rust, and an oak tree started growing. It was too close to the house, but I let it gow anyhow. By the second summer I realized it was a weed. It had no real trunk.

OTOH, I have two tulip trees (I forget the other name for them) that just started growing on their own. One is 45 feet tall or more and the other is only 4 years or so and is 25 feet tall. The first is very near a pine tree that got killed by a variety of problems, so that's good.

You are talking about a Poplar. That is a weed too, as are oaks around here. I mow down hundreds every year from squirrels burying acorns. There are 3 here at my house that came up wild since I moved here and they are huge.

There's an Android app named PlantSnap that gives you give five free look ups. You take a picture, upload to their server, it tells you what kind of plant it is. You can get a lifetime subscription for $16.

it will become obvious when it grows another six inches.

Great pictures!