A new solution is available using the styled mode for Highcharts. You can refer to this example: http://jsfiddle.net/brightmatrix/u4mhpg9o/
I made an interesting discovery regarding customizing the connector width for data labels in Highcharts. By applying a local style to the specific color assigned to your data label or any other custom style you create, you have the ability to adjust the connector width. In my case, I modified the width of the connector for pie slice #7 in the chart's stylesheet (avocados):
/* style defined in the demo for all connectors */
.highcharts-pie-series .highcharts-data-label-connector {
stroke: silver;
stroke-dasharray: 2, 2;
stroke-width: 2px;
}
/* local style just for connector #7 */
.highcharts-data-label-connector + .highcharts-color-7 {
stroke-width: 20px;
}
The outcome can be seen here:
https://i.sstatic.net/9s9kG.png
You can identify which style name corresponds to each pie slice by inspecting the code in your web browser.
If you are not utilizing the styled mode, changing the connector width is limited to the series level and cannot be done for individual data points.
This information should provide some helpful insights for you.