Sure, you can't argue that Toyota doesn't have the credibility and knowledge to build it as a PHEV and it already has a suitable engine from the GR Yaris, but i still think it would add substantial weight and perhaps more importantly the packaging and placement of that weight over the current gen.
BMW's i8 uses a similar short range battery and motor with a 3cylinder ICE to make it a 992 rival. But to keep its weight competitive it has a CF passenger cell. You can't go that exotic with a $32-40k car.
The I8 is not a small car, and it has 4 seats and is a pretty luxurious package. I don't think they went far out of their way to make it super light. The I8's battery weighed 100kg and was around 10kwh. That's a density of 10kg/kwh. Remember, the all-carbon and non-electrified Ford GT also weighed over 3,000lbs.
Tesla's P100D battery weighed 625kg for 100kwh for a density of 6.25kg/kwh
If you use the current state of the art (its another subject on whether or not Toyota would go Li or not) you could get a 10kwh battery at around 70kg (154lbs) I'd guess.
Now if we take the FA24 engine - it's a good engine in terms of having low CG, but it's inefficient in that it has 2 heads, 4 cams, etc since it has two "banks" of cylinders. It's NOT a light engine, somewhere north of 420lbs without the transmission from what I can find. The Yaris GR engine weighs just 240lbs!
240lb engine + 154lb battery = 394lbs. If we add in the electric motor, we're probably a little more than the FA24, but not drastically so. The 3 cylinder is great for packaging, and if the platform is designed from the onset as a PHEV, I'm guessing Toyota could find a performance-enhancing place to mount the battery. I would actually prefer the hypothetical PHEV to operate both in series and parallel so that you could run on EV only or use the motor to boost the ICE low end torque in kill mode - all power going to the rear wheels.
So we would end up with a car that is not much heavier than the current one, but with potentially more centralized mass, and critically, more room for better suspension geometry up front (that FA24 is a wide boy).
edit: fixed typos