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We study associate and double associate spaces of two-weighted Sobolev spacesof the first order on real half-line and we show that unlike the notion ofduality the associativity is divided into two cases which we call "strong" and"weak" ones with the division of the second associativity into four cases. Onthe way we prove that the Sobolev space of compactly supported functionspossess weak associated reflexivity and the double weak-strong associate spaceis vacuous. The case of power weights was recently characterized by reductionto Ces\`{a}ro or Copson type spaces [18].

On weak associated reflexivity of weighted Sobolev spaces of the first order on real line