Help me pick a new desktop speaker

My nephew has desktop Elacs. I doubt you would go wrong with them!

I know you mentioned doing passive speakers with a separate amp, but I would really look at active or powered options as well. For example the Adam Audio D3V is a really small powered system with a built-in USB DAC. For $300 those little things sound amazing for nearfield listening.

You could also go bigger and get their T7V which is around $250 each so $500/pair. Larger in both size and sound, they also sound really great for the price, and still come in below your 20lb weight limit. 

I was worried about active monitors sounding to sterile but after hearing these Adams I changed my mind. They are very enjoyable. 

Check out the new Elac Debut 3.0 DB63. I wrote a review on here recently that nobody seemed interested in. I am very happy with these speakers and I've gone through about 20 of them in the last 10 years. 

You mentioned passive speakers but the Vanatoo active speakers are very good.

For your price range, i would go with a Yamaha HS8 active monitor for around ~700-ish (no amp needed). Set it on stands on either side of your desktop. It is not some sterile sounding monitor, but a very musical speaker.

You could put it on something like a Schiit Jotunheim (R2R dac + preamp) and have some high quality sound, i.e. you would need to spend a lot more to beat that level of sound whilst sitting nearfield or midfield.

The Andrew Jones Elacs typically need a higher quality amp, etc (might fall outside your price range) to reap their full potential.

I am a picky audiofool and dont want to thru a merry go round.