...my needle bounces all the way over...
What needle? The one on the radio. Of course, it's measuring the radio power. It cannot measure the amplifier power.
...how much more could I safely drive it with w/o frying it...
Disclaimer: Any such amplifier used in the CB service in the US (and many other places) is very illegal.
The RM Italy site says 10W in for 100W out for AM or FM, 20W in for 200W out PEP using SSB. That's 10dB power gain. Sounds about right for the size of the thing. That means it is made to deliver 200W PEP with 20W input. That's how hard you can drive it without frying it. But like anything else running at full blast all the time is not the best idea.
If you drive it with 2W AM carrier you should expect around 20W out. Gain may well be non-linear across it's range.
Keep in mind for *standard* AM the total power is 4 times the carrier power. Your 4W radio actually would make 16W of power for full modulation AM. However, US law restricts the average power dissipation of the output device to 10W. This is where we get to the difference between peak, peak envelope, and average power which I won't go in to; and distortion from over-modulation and the difference between consumer class equipment and amateur and professional.
Moreover, US law requires commercial amplifiers approved for sale in the amateur service to exhibit NO amplification for CB frequencies. I doubt this amplifier complies with said law.
If this is a typical 13 db gain amp it will more than double your range twice. It takes 6 dB gain to double your range,
Double range is subjective. Line of site transmissions which is what 27MHz CB is intended to be will not see a double of range as such once the signal is already beyond the radio horizon. This also assumes the antenna system gets all the power into the air.
You'll do much better with good audio, an efficient antenna system, and good height than just adding power. Most CB shop's *peaking* just makes a mess.