WebView leaks WCImgDecoderImpl instances that are often very large. The simplest example can be used to demonstrate the problem:

import javafx.application.Application;
import javafx.event.ActionEvent;
import javafx.event.EventHandler;
import javafx.scene.Scene;
import javafx.scene.control.Button;
import javafx.scene.control.Label;
import javafx.scene.layout.BorderPane;
import javafx.scene.web.WebView;
import javafx.stage.Stage;

public class Main extends Application {

    final BorderPane borderPane = new BorderPane();
    Button button = new Button();

    @Override
    public void start(Stage primaryStage) throws Exception {
        final WebView webView = new WebView();
        webView.getEngine().load("http://www.livewirelabs.com.au");
        borderPane.setCenter(webView);

        button = new Button("Remove");
        button.setOnAction(new EventHandler<ActionEvent>() {
            @Override
            public void handle(ActionEvent actionEvent) {
                borderPane.setCenter(new Label("Gone"));
            }
        });
        borderPane.setBottom(button);
        primaryStage.setScene(new Scene(borderPane, 500, 600));
        primaryStage.show();
    }

    public static void main(String[] args) {
        launch(args);
    }
}

Push the button and use MemoryAnalyzer to identify the leaked instances. 

I am attaching MemoryAnalyzer screen shots of the issue manifesting itself in our production application. The data in these shots is from 4 WebView instances (that no longer exist in heap) loading a single page (http://www.bloomberg.com/markets/).

https://www.evernote.com/shard/s149/sh/4d37f473-a5e4-4663-830e-5f93d9a158c9/ae2db406d1d2766e9f36c52ee4af6936

https://www.evernote.com/shard/s149/sh/e7bb0597-e99a-4853-a151-9d21916bc0fa/776a03044248b2b9e9551791352f9865

https://www.evernote.com/shard/s149/sh/97641ccd-ef46-40cc-a949-21618e2a4ea7/c0fc4e4a138c64b7e5c485e8411048f5

https://www.evernote.com/shard/s149/sh/73a6da5b-6d24-443f-af73-5b0b01b3b33a/c88f025f6a1113ec3f8d60ead6d07b75