Quite a difficult task actually.
Typically high zoom range scopes of good quality yet light weight are typically expensive.
A Leupold VX3 should be great glass but will either be 3.5-10 or 4.5-14, will be under weight but will probably have to import from the US.
A Nikon Monarch 3 3-12 or 4-16 will also be great glass, a little over weight, but under budget.
A Vortex Viper HS in 4-16 will be over weight, but good glass and under budget.
A Ziess Conquest will be over budget, excellent glass and possibly under weight.
A Swarvorski Z3 3-10 will be under weight but over price but excellent glass.
A Leupold VX6 2-12 would be great glass, great zoom range under weight, but too expensive.
A 3-9 in a Bushnell, Burris, Leupold or Nikon will be under weight, good glass and right price but not the best use of your budget (which may or may not be a bad thing).
I think the defining factor will be the defining factor. If you are happy with a 3-9 it'll be easy to find something.
If you want a 3-12 or 4-12 or 4-16 or 3-15 then you will have to spend more money to get it under budget, or but up with more weight.
Will probably have to import something from the US to get best value for money.
If I were in your position, I'd probably look for a Leupold VX3 or VX2 and put up with less zoom range, should find under budget.
Or put up with more weight and go for a Nikon Monarch 3 3-12 or 4-16.
Actually a Sightron SII 4-16 should meet all those requirements.
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