Check out the Object > Transform > Transform Each command.
Make your selection and then open the transform each dialog where you can input the scale percentage. Notably, since you mentioned objects with different stroke weights, look at the option at the bottom left for "Scale Strokes and Effects". If that is checked, then the strokes will be scaled to match the scale percentage you gave at the top. if that box is not checked, the strokes will remain exactly the same size even as the objects get scaled.