What weight can a tri-axle straight truck haul Light weight of truck is 23000 class 7?

Negative. That IS NOT a Class 7 truck... truck classification is based on the Gross Vehicle Weight Rating, NOT the tare (empty) weight of the vehicle. That is a Class 8 truck.

Other than that, it varies according to a number of factors. Wheelbase, what type of road it's on (a lot of states permit a higher weight on secondary roads), what type of axle the lift axle is (23k axle with dual tires vs. a 10k steerable pusher, etc), and so forth. What you're looking at, with that tare weight, most likely between 15 and 18 tons is what it could legally haul, depending on the above factors.