Application.Resources.xaml

<Application.Resources>
    <DataTemplate x:Key="DateTemplate" DataType="{x:Type system:DateTime}">
        <TextBlock Text="{Binding Date}"/>
    </DataTemplate>

    <DataTemplate x:Key="DayOfWeekTemplate" DataType="{x:Type system:DateTime}">
        <TextBlock Text="{Binding DayOfWeek}"/>
    </DataTemplate>
</Application.Resources>

GridViewColumn.Width.cs

public static class GridViewColumn
{
    private static readonly GridLength _defaultValue = new GridLength(0, GridUnitType.Auto);
    private static readonly Dictionary<System.Windows.Controls.GridViewColumn, GridVieColumnWidthInfo> _columns = new Dictionary<System.Windows.Controls.GridViewColumn, GridVieColumnWidthInfo>();

    public static readonly DependencyProperty ColumnWidthProperty =
        DependencyProperty.RegisterAttached("ColumnWidth", typeof(GridLength), typeof(GridViewColumn), new PropertyMetadata(_defaultValue, OnWidthChanged));

    /// <summary>
    /// Sets the value of the attached property ScrollGroup.
    /// </summary>
    /// <param name="obj">Object on which the property should be applied.</param>
    /// <param name="gridLength">Value of the property.</param>
    public static void SetColumnWidth(DependencyObject obj, GridLength gridLength)
    {
        obj.SetValue(ColumnWidthProperty, gridLength);
    }

    /// <summary>
    /// Gets the value of the attached property ScrollGroup.
    /// </summary>
    /// <param name="obj">Object for which the property should be read.</param>
    /// <returns>Value of the property StartTime</returns>
    public static GridLength GetColumnWidth(DependencyObject obj)
    {
        return (GridLength)obj.GetValue(ColumnWidthProperty);
    }

    /// <summary>
    /// Occurs, when the ScrollGroupProperty has changed.
    /// </summary>
    /// <param name="d">The DependencyObject on which the property has changed value.</param>
    /// <param name="e">Event data that is issued by any event that tracks changes to the effective value of this property.</param>
    private static void OnWidthChanged(DependencyObject d, DependencyPropertyChangedEventArgs e)
    {
        if(!((GridLength)e.NewValue).IsStar)
            throw new ArgumentException("ColumnWidth must be starsize");
        var column = (System.Windows.Controls.GridViewColumn)d;
        column.
        if (_columns.ContainsKey(column))
            return;
        var info = new GridVieColumnWidthInfo()
        {
            Column = column,
            Width = GetColumnWidth(d)
        };
        _columns.Add(column,info);
        var binding = new Binding
        {
            RelativeSource = new RelativeSource(RelativeSourceMode.FindAncestor, typeof(Selector), 1),
            Converter = new GridViewColumnWidthConverter(),
            ConverterParameter = info
        };
        BindingOperations.SetBinding(column, System.Windows.Controls.GridViewColumn.WidthProperty, binding);
    }

    private class GridVieColumnWidthInfo
    {
        private Selector _parent;
        private GridViewColumnCollection _columns1;
        public System.Windows.Controls.GridViewColumn Column { get; set; }
        public GridLength Width { get; set; }

        public Selector Parent
        {
            get { return _parent; }
            set
            {
                _parent = value;
                _parent.AddHandler(FrameworkElement.SizeChangedEvent, new SizeChangedEventHandler(PanelSizeChanged));
                BindingOperations.ClearBinding(Column, System.Windows.Controls.GridViewColumn.WidthProperty);
            }
        }

        public GridViewColumnCollection Columns
        {
            get { return _columns1; }
            set
            {
                _columns1 = value;
                foreach (var col in _columns1)
                {
                    PropertyChangedEventManager.AddHandler(col, (sender, args) => Update(),"ActualWidth");
                }
                CollectionChangedEventManager.AddHandler(_columns1, Handler);
            }
        }

        private void Handler(object sender, NotifyCollectionChangedEventArgs e)
        {
            if (e.NewItems != null)
            {
                foreach (var col in e.NewItems.Cast<System.Windows.Controls.GridViewColumn>())
                {
                    PropertyChangedEventManager.AddHandler(col, (o, _) => Update(), "ActualWidth");
                }
            }
            if (e.OldItems != null)
            {
                foreach (var col in e.OldItems.Cast<System.Windows.Controls.GridViewColumn>())
                {
                    PropertyChangedEventManager.RemoveHandler(col, (o, _) => Update(), "ActualWidth");
                }
            }
        }

        private void PanelSizeChanged(object sender, SizeChangedEventArgs sizeChangedEventArgs)
        {
            Update();
        }

        private void Update()
        {
            var notSet = Columns.Where(x => GetColumnWidth(x) == _defaultValue);
            var sum = notSet.Select(x => x.ActualWidth).Sum();
            var starSized = Columns.Where(x => GetColumnWidth(x).IsStar);
            var totalStarWidth = Parent.ActualWidth - sum;
            var totalStarValue = _columns.Where(x=>starSized.Contains( x.Key)).Sum(x=>x.Value.Width.Value);
            Column.Width =(Width.Value/totalStarValue) *totalStarWidth; 
        }
    }
    private class GridViewColumnWidthConverter : IValueConverter
    {
        public object Convert(object value, Type type, object parameter, CultureInfo culture)
        {
            var info = (GridVieColumnWidthInfo)parameter;
            var listView = (ListView)value;
            info.Parent = listView;
            info.Columns = ((GridView)listView.View).Columns;
            return info.Column.ActualWidth;
        }

        public object ConvertBack(object o, Type type, object parameter, CultureInfo culture)
        {
            throw new NotSupportedException();
        }
    }
}

Xaml.xaml

<ListView>
    <ListView.View>
        <GridView>
            <GridViewColumn Header="Day"
                            CellTemplate="{StaticResource DayOfWeekTemplate}"/>
            <GridViewColumn Header="Date" 
                            ap:GridViewColumn.ColumnWidth="*"
                            CellTemplate="{StaticResource DateTemplate}"/>
        </GridView>
    </ListView.View>
    <system:DateTime>2014-01-01</system:DateTime>
    <system:DateTime>2014-01-02</system:DateTime>
</ListView>