Light, strong and cheap.. pick any two (haven't we all heard this?). For $1600 your not going to get a very light bike that can stand up to real trail riding/All mountain riding/ Aggresive XC/ ye olde freeriding/etc..
I'm about your weight, and although I can't get away with some lighter parts, I still feel a light weight rider can break the same parts as a heavier rider (may just take something bigger or a little longer).
Start with a frame that is light for it's strength and get yuorslef a cheap/mid level build kit. Spend more on fork and frame and then as you get money upgrade to lighter parts.
Other option would be to get a cheap XC racing dually and to slowly make it more suited to trail riding..
Either way.. it will be difficult to get a bike for $1600 below 28lbs without giving up All mountain performance..