Will you mainly be pitching on grass rather than rock/mountain?
Mostly for fairer weather and not winter?
If so, you don’t need to worry about getting anything particularly technical/fancy, which will make hitting your weight and budget a lot easier.
Tunnel tents will probably offer the greatest volume to weight ratio. When you say you want “smallish”, I presume you mean pack size rather than wanting a lack of room for you, your wife and dog? In any event, at 2kg, you’re not going to be getting a castle!
Wild Country Hoolie is around that weight, size and budget.
Vango Banshee 300 is another option, although will come in a bit over your weight.
Ignore the stock STW response of a Zephyros 2, unless you and your wife are midgets and your dog is actually a gerbil.