My computer, which is NOT a laptop, but rather a mid-tower (think small beige box) weighs about the same as two of my karaoke books. My monitor, a small flat old ViewSonic LCD I bought at a thrift store 3 years ago for $30, weighs quite less than one of my karaoke books. Where I have my dongles in place to the house PA & TVs, Setup time is about 3 minutes. Sorry, I don't see where weight and setup time is an issue in tower vs. laptop.
As far as mobility, I've been running this way for years, and did not drive. I took the city bus to and from my gigs, moving my karaoke gear in a crate with wheels I got at Staples for $20. Currently my karaoke system fit well in the passenger seat of my '91 Honda CRX. My solution is simple: I only book gigs at clubs & bars that already have a house PA suitable for bands and also already have TVs. When I get the gig, I come in and place all the cables and adapters in place to connect my karaoke system to it then leave them there. My rig is simple: my computer, two wireless mic receivers, my mics, an Alesis NanoVerb effects processor, and my karaoke books. By far the most bulky and heavy thing is my books. In the past I've printed extra copies and stored them at my various venues so I would not have to transport them on the bus. Before I got my small LCD flat-panel monitor, I did the same with 17" CRT monitors. Not a big deal, they're only around $5 each at thrift stores here.
I've got shockingly little money in my equipment, running mostly old junk from thrift stores. I've instead chosen to spend all my money on an amazing karaoke music library, and invest my time into making very impressive organized karaoke books. This is what has kept me booked 3-7 nights a week in top venues for the last 5 years.
-- Dan Dan