The aim of this paper, we introduced some result of best co-approximation specifications of co-proximal and co-chebyshev of unbounded functions in weighted spaces. Also, we discuss some properties of best co-proximal and Co-chebyshev of un bounded functions which gives basic definitions and necessary concepts are convexity, orthogonlity and closed which helps us in the proofs of main results. In addition to that verification, when the function is multiplied by a constant, it maintains its properties.