Before the advent of Tarptents and tents like the Fly Creek 1 and Carbon Reflex 1, I regularly used an Integral Designs Salathe Bivy - and a silnylon tarp. I found the bivy minimally useful without the tarp, since you had nowhere to cook or change clothes otherwise. Adding the weight of the bivy and tarp, I was at 3 pounds - within a few ounces of the Carbon Reflex 1 tent I use now.

Which do I prefer? Well, the CR1 allows me to sit up inside the shelter, even when it's in bug mode only; the bivy/tarp combo only let me sit up if I unzipped the mesh. The CR1 is better ventilated in the summer, but a bit cooler in the winter; spring and fall are a wash. The tarp/bivy combo allowed me to set up the tarp first, then deploy the bivy out of the rain. The CR1 may be pitchable fly-first, but that may require using the groundcloth (which adds a quarter pound) - I just haven't played with it that way yet, so I can't say for sure. The tarp could be pitched alone to make a lunch shelter; the CR1 fly can be pitched with the ground cloth to do the same (but there's that pesky extra weight again.)

Personally, I've settled on a solo tent in preference to a tarp/bivy combo, but it was a close call, probably driven as much by subjective preference as objective features.

Eliminate the tarp, and the choice becomes much easier: I'll take the tent over a tarpless bivy every time, even if it does weigh more.