DragResizerXY can be used to add mouse listeners to a Region and make it resizable by the user by clicking and dragging the border in the same way as a window. Height and Width are both working.

DragResizerXY.java

import javafx.event.EventHandler;
import javafx.scene.Cursor;
import javafx.scene.input.MouseEvent;
import javafx.scene.layout.Region;

/**
 * {@link DragResizerXY} can be used to add mouse listeners to a {@link Region}
 * and make it resizable by the user by clicking and dragging the border in the
 * same way as a window.
 * <p>
 * Height and Width resizing is working (hopefully) properly
 * 
 * <pre>
 * DragResizer.makeResizable(myAnchorPane);
 * </pre>
 *
 * @author Cannibalsticky (modified from the original DragResizer created by AndyTill)
 *
 */
public class DragResizerXY {

	/**
	 * The margin around the control that a user can click in to start resizing
	 * the region.
	 */
	private static final int RESIZE_MARGIN = 10;

	private final Region region;

	private double y;

	private double x;

	private boolean initMinHeight;

	private boolean initMinWidth;

	private boolean draggableZoneX, draggableZoneY;

	private boolean dragging;

	private DragResizerXY(Region aRegion) {
		region = aRegion;
	}

	public static void makeResizable(Region region) {
		final DragResizerXY resizer = new DragResizerXY(region);

		region.setOnMousePressed(new EventHandler<MouseEvent>() {
			@Override
			public void handle(MouseEvent event) {
				resizer.mousePressed(event);
			}
		});
		region.setOnMouseDragged(new EventHandler<MouseEvent>() {
			@Override
			public void handle(MouseEvent event) {
				resizer.mouseDragged(event);
			}
		});
		region.setOnMouseMoved(new EventHandler<MouseEvent>() {
			@Override
			public void handle(MouseEvent event) {
				resizer.mouseOver(event);
			}
		});
		region.setOnMouseReleased(new EventHandler<MouseEvent>() {
			@Override
			public void handle(MouseEvent event) {
				resizer.mouseReleased(event);
			}
		});
	}

	protected void mouseReleased(MouseEvent event) {
		dragging = false;
		region.setCursor(Cursor.DEFAULT);
	}

	protected void mouseOver(MouseEvent event) {
		if (isInDraggableZone(event) || dragging) {
			if (draggableZoneY) {
				region.setCursor(Cursor.S_RESIZE);
			}

			if (draggableZoneX) {
				region.setCursor(Cursor.E_RESIZE);
			}

		} else {
			region.setCursor(Cursor.DEFAULT);
		}
	}
	
	
	//had to use 2 variables for the controll, tried without, had unexpected behaviour (going big was ok, going small nope.)
	protected boolean isInDraggableZone(MouseEvent event) {
		draggableZoneY = (boolean)(event.getY() > (region.getHeight() - RESIZE_MARGIN));
		draggableZoneX = (boolean)(event.getX() > (region.getWidth() - RESIZE_MARGIN));
		return (draggableZoneY || draggableZoneX);
	}

	protected void mouseDragged(MouseEvent event) {
		if (!dragging) {
			return;
		}

		if (draggableZoneY) {
			double mousey = event.getY();

			double newHeight = region.getMinHeight() + (mousey - y);

			region.setMinHeight(newHeight);

			y = mousey;
		}

		if (draggableZoneX) {
			double mousex = event.getX();

			double newWidth = region.getMinWidth() + (mousex - x);

			region.setMinWidth(newWidth);

			x = mousex;

		}

	}

	protected void mousePressed(MouseEvent event) {

		// ignore clicks outside of the draggable margin
		if (!isInDraggableZone(event)) {
			return;
		}

		dragging = true;

		// make sure that the minimum height is set to the current height once,
		// setting a min height that is smaller than the current height will
		// have no effect
		if (!initMinHeight) {
			region.setMinHeight(region.getHeight());
			initMinHeight = true;
		}

		y = event.getY();

		if (!initMinWidth) {
			region.setMinWidth(region.getWidth());
			initMinWidth = true;
		}

		x = event.getX();
	}
}

Thanks for this! If a prefHeight/prefWidth are set on the region they will currently act as a minimum, at least on the BorderPane I was just trying it with. If you add region.setPrefHeight(newHeight) etc into the mousePressed method it will overcome this limit.

Thank you for that! It was very useful to me. I also had the need to move the component with the mouse. So I made some changes, adding that too. If someone wants it, below is the link to the file.
https://gist.github.com/rutsatz/bb80e9535ff665276c5128260428eaa8
Hugs!