When you copy a clip from one sequence to another, the clip inherits the dimensions of the sequence it was pulled from. This will be apparent if you copy form a sequence with a different frame size than the one you are pasting into.
If you want to resize the clip back to the native frame size of the source clip, then after you paste it into the new sequence, control-click on the pasted in clip and select Remove Attributes from the drop down menu. Once the Remove Attributes Pane opens, check the boxes for Basic Motion and Distort (if they are not grayed out) and click OK.
You can use this procedure on multiple clips by selecting the clips you want to change and control clicking on any one of those selected clips.