Yes, this works

Weapons with the thrown property still appear on the Weapons table, and are still classified as simple or martial weapons. As such, the arcane weapon spell can channel energy into them.

Note that the specification of "a weapon you're holding" only matters when the spell is cast; nothing in the spell description says the spell ends if the weapon leaves your hand. As such, once you cast arcane weapon on any simple or martial weapon that you're holding, the spell remains active on that weapon for up to an hour as long as you maintain concentration - even if you sheathe the weapon, drop it, or throw it.

Normally, it might not be very useful to use the spell with thrown weapons, as you wouldn't normally have a way to get the weapon back after you throw other than going and picking it up - but the Returning Weapon infusion causes the weapon to return to your hand after you make a ranged attack (presumably a thrown one) with it, so you can keep doing this every turn.

Yes, but it's not perfectly smooth

Currently, as described, there are three ways to drop an infusion.

• You can die, and wait a few days. This will cause you to drop all of them all at once, and also requires you do die and stay dead for a few days. It's not a perfect solution.

• You can infuse enough items to exceed your maximum, thus causing your oldest to fall off the back end. Since you can keep touching and keep reinfusing, you can easily decide whichever distribution you like every day. Just re-infuse until you've dropped the ones you want to drop. This is potentially problematic in the case where you have infusions (like your favorite Bag of Holding) that you don't want to drop for even a moment, but otherwise works quite well.

• On level-up, you can unlearn one infusion in favor of another, which instantly drops the infusion on whichever one you unlearned. This has obvious limitations on frequency of use, but does let you drop any one infusion cleanly without disrupting any other.

On the other hand, this is UA

UA is playtest material, and they generally won't have caught everything. They haven't considered all of the edge cases. If this is a real issue for you, you can, and should, consult with your DM about it (who should be paying careful attention to balance issues on all UA material to begin with, and adjusting as necessary for their personal campaign) and ask for the ability to decide which infusion you drop when infusing past your max at the end of a long rest. It would be a convenience increase without meaningful power increase. As a DM, I'd permit it.