Some of my variable shows weak collinear relationship on my dependent variable.. how should I address this?
Your question contains very little information so these are my two cents. Assuming your model is correctly specified and there is no underlying problem with the data you are using, there's really little you can do about this. In my experience, this is often the case where some variables are included based on the literature and the relationship found in the regression model does not necessarily reflect the hypothesized relationships. Now, assuming you are studying a relationship based on some theoretical work and that your sample isn't small (so as to have a negligible effect of insignificant variables on p-values), you should not drop variables (this is the equivalent as specifying a theoretical relationship based on the results of a regression model and it is, from a purely academic perspective, the wrong direction to work in). This is generally the case where these variables have a hypothesized relationship as predictors or serve as controls. When deciding whether the addition of these variables may create a problem in the OLS estimation you may try to run different regressions adding and excluding those variables to see if there are any important changes (e.g. in the variance explained by your model or in the overall fit). Now, as I said, there is little information provided, so I am assuming many things here.