From the type of riding you are describing you are doing, would be looking more at mid range XC bike, this won't be 'lightweight' but should come in between 25-28lbs, to be within your budget, most MTB's now have Aluminum frames, which are not normally narrow diameter tubes (steel tubes are narrow) for 'narrow wheels', am reading this as tires, tires normally start at 2.1 now, and go up, the days of narrow tires are long gone.

Plenty of bikes out there, you need to decide what wheel size you want, there are the options of 26", 27.5 or 29ers if you are tall, would look for warranty provision, brands like Trek and Specialized are good for this, and where you are going to get it from, if from a LBS, what added value do they offer over mail order, fitting, setup, after sales etc