I'll chime in, I provided Power In Motion with assistance and feedback on the project, and had a fun run with the bike. Its a very good little bike, I liked the end result quite a bit. The electric system does not interfere with the folding in any way, the bike was very quick and responsive. The price on that one would be slightly over your $2,000 budget, I believe.
That Tikit in particular is using a Crystalyte motor, but not the typical 405 / 408s you see on most bikes. It ended up being quite a bit lighter than the 40X series of Crystalyte motor, that Tikit is still very reasonably light - comparable to a BionX.
You can contact someone at Power In Motion for information on that motor, they can certainly obtain it for you.
They have a US storefront @ http://us.itselectric.ca/
For an electric motor at a lower price point, I recommend Crystalyte. They are fairly basic, operated just by a thumb throttle, with no special features or frills. But, their functionality is very good, they are very reliable, and extremely customizable. You can buy any kind of battery, controller, throttle, many accessories, easy to get parts and supplies for. Although there is no automatic pedal assist, the rider can still pedal along and get assist using the throttle quite easily.
Normal Crystalyte setups are 7-8lbs heavier than a BionX overall, due to the motor being heavier. But for a simple "guest bike", you could quite easily purchase a Dahon or other decent, affordable folder and pair it with a Crystalyte for a reasonably priced but very good little bike.
If you are interested in Crystalyte kits, they are obtainable starting at around $475, and then a battery is on top of that in cost. For a 20" wheel, the Crystalyte 405 is what you would want, or possibly the smaller, lighter 24v Crystalyte motor seen on the e-tikit . And on a Dahon, you would want a rear wheel kit, as the front wheel kit would not fit in the dropouts.
Batteries are where lots of weight can come into play. Lithium batteries are certainly top of the line, very light options with good power and range are available these days. Their economy is becoming pretty good, with long service lives. The only downside is the entry cost into this battery type, but these are the key to having lighter e-bikes.
And, regarding the BionX system mentioned by ThorUSA, it is also a very good option. They are lighter than the standard Crystalyte 40X series by 7-8lbs, and come with more features and perks. They have a command console that displays speed, distance, time, and remaining battery, a very organic and precise feeling pedal assist system, e-brakes, and some other small perks.
I recommend this system if you are looking for the rolls royce of the e-bikes. The biggest downside to the BionX though, is that the system is closed and proprietary - a Crystalyte or other e-bike user can purchase 3rd party batteries, accessories, and change their systems design as needed, whereas a BionX user is more locked in to the design. And their replacement batteries are particularly pricey. Its a great system as long as you are happy with what you get out of the box, and don't mind paying more for batteries down the road. Very class e-bike design.