You could achieve this with the use of anchors. Or more precisely the non use of them.
Controls are anchored by default to the top left of the form which means when the form size will be changed, their distance from the top left side of the form will remain constant. If you change the control anchor to bottom left, then the control will keep the same distance from the bottom and left sides of the form when the form if resized.
Turning off the anchor in a direction will keep a control centered when resizing, if it is already centered. In general, a control not anchored maintains its proportional position to the dialog. E.g. If you put a control at X=75% of the dialog width and turn off left/right anchors, the control will maintain its center at X=75% of the dialog width.
NOTE: Turning off anchoring via the properties window in VS2015 may require entering None (instead of default Top,Left)