Sounds to me like you need an accurate pressure regulator with a gauge, a miniature one, more than adequate for airbrush use, here in the US can be had for 30 dollars or so, plus whatever fittings are needed.
Siphon feed Airbrushes like yours need the higher pressure to pull the paint up out of the cup or jar, you should, however, be able to paint reasonably fine lines with it. For the really fine hairlines you would need a gravity feed airbrush, with the paint cup on top, which as the name implies, the paint is fed by gravity, therefore requiring much less air pressure, as little as 5 psi for some.