Weighing less you say? Okay, let's do the math.
F-5E empty weight - 4349kg.
MiG-19P empty weight - 5673kg.
Fuel mass for 5E/19P - 2050/1800kg.
Fueled weight - 6399/7473. MiG-19P is still one tonne more. Not talking about weight of missiles and ammo, wich is +- the same.
Let's stand that they will enter the dogfight fully fueled. And - oops - MiG-19 looses its engines only after 8 minutes of full burner due to fuel consumption - its RD-9BF engines consume 12375kg of fuel per hour, compared to only 9567 of Tiger. Its fuel allows it to dogfight for nearly 13 minutes. So, to ensure equiality, we must lower the fuel ammount F-5 should use. For 8 minutes of burner it needs only 1261kg of fuel. So, its fueled weight should be 5610kg. Nearly 2 tonnes less then MiG-19P.
With this weight it has T/W ratio of 0.808. Fueled MiG-19P has T/W ratio of 1.007. Well, it is still has more T/W then Tiger, but, as experiments with MiG-21/23 have shown, T/W did not play much role in dogfighting with Tiger. MiG-23MLs used in it had T/W nearly 1.1 and still lost. And all because of wing mechanisation. Moreover, MiG-19P was never meant to do dogfighting, it is an interceptor. So it is needless to wait some king of maneuverability from it.