Exactly like that...

Any help would be appreciated.

Thanks.

AP

1. Custom TilePane
We need properties that control the height and position of a TilePane relative to the tile dimensions
The HeightFactor  is used to calculate a tile height relative to the uniform cell (normal size)
The VerticallOffsetFactor is used to position a tile relative to the normal position.
public class MyTilePane : TilePane
{
  public double HeightFactor { get; set; }
  public double VerticalOffsetFactor { get; set; }
  protected override Size MeasureOverride(Size availableSize)
  {
    if (!double.IsInfinity(availableSize.Height))
    {
      // The availableSize is a uniform cell size
      availableSize.Height *= this.HeightFactor;
    }
    Size sz = base.MeasureOverride(availableSize);
    return sz;
  }
}

2. Custom TilePanel
We need to arrange a tile in a rectangle that has different height and position  (according the height and vertical offset factors).
public class MyTilePanel : TilePanel
{
  private bool _hasMaximized;
  protected override Size MeasureOverride(Size availableSize)
  {
    this._hasMaximized = false;
    foreach (TilePane tile in this.Children)
    {
      if (tile.TileState != TileState.Normal)
      {
        this._hasMaximized = true;
        break;
      }
    }
    return base.MeasureOverride(availableSize);
  }
  protected override void ArrangeChild(UIElement element, Rect finalRect, bool useAnimation)
  {
    if (!this._hasMaximized)
    {
      MyTilePane tile = element as MyTilePane;
      if (tile != null)
      {
        finalRect.Y += tile.VerticalOffsetFactor * finalRect.Height;
        finalRect.Height *= tile.HeightFactor;
      }
    }
    base.ArrangeChild(element, finalRect, useAnimation);
  }
}

3. XamWebTileView control template
Open your page in Blend, edit the XamWebTileView template to create a new style and replace TilePanel with MyTilePanel
the original line is something like this: <igPrim:TilePanel x:Name="PagePanel"
and the new line should be: <local:MyTilePanel x:Name="PagePanel"
Finally your code will look like this:
<igTV:XamWebTileView x:Name="tv3" RowsInPage="2" ColumnsInPage="3" 
Style="{StaticResource MyTileViewStyle}"
TileDragCompleted="tv3_TileDragCompleted"
>
<local:MyTilePane Header="1" Content="1" HeightFactor="0.5" VerticalOffsetFactor="0"/>
<local:MyTilePane Header="2" Content="2" HeightFactor="1.5" VerticalOffsetFactor="0"/>
<local:MyTilePane Header="4" Content="4" HeightFactor="0.5" VerticalOffsetFactor="0"/>
<local:MyTilePane Header="3" Content="3" HeightFactor="1.5" VerticalOffsetFactor="-0.5"/>
<local:MyTilePane Header="6" Content="6" HeightFactor="0.5" VerticalOffsetFactor="0.5"/>
<local:MyTilePane Header="5" Content="5" HeightFactor="1.5" VerticalOffsetFactor="-0.5"/>
</igTV:XamWebTileView>

4. Drag and Drop
Drag and Drop replaces positions of two tile and we need to recalculate offset and height factors:
private void tv3_TileDragCompleted(object sender, TileDragCompletedEventArgs e)
{
  MyTilePane tile1 = e.DragElement as MyTilePane;
  MyTilePane tile2 = e.TargetElement as MyTilePane;
  if (tile1 != null && tile2 != null)
  {
    double t;
    t = tile2.VerticalOffsetFactor;
    tile2.VerticalOffsetFactor = tile1.VerticalOffsetFactor;
    tile1.VerticalOffsetFactor = t;
    t = tile2.HeightFactor;
    tile2.HeightFactor = tile1.HeightFactor;
    tile1.HeightFactor = t;
  }
}

It is all. I'm going to attach the full solution but right now I'm busy.
This sample produces the following result:

Hello. Where can I download the solution for this post? I'm having similar problem. Thank you

Thanks Marin, this is very helpful.

I'll try putting the pieces together this afternoon.