I think the problem is here:

//simply find the node higher weight than the one you are inserting
while (current != null && (current.getPerson()).getWeight() < x.getWeight()) {
    current = current.getNext();
}

If current.getPerson().getWeight() has a higher weight than any other node, then it is going to keep looping until the other condition (current != null) is false. So in this case, current will be null at the end of that while loop.

The if statement on line 13 doesn't match, since there is already a single node in the list. But then the problematic statement on line 17 comes up. Since current is null, trying to execute current.getPrevious() will always give a null pointer exception. You may want to test to see if current is null and if so, then append pn to the end of the list.

I struggled with this same problem a couple years ago. Unfortunately, I found no real solution (maybe Java 1.7 changed things?).

The only solution I could find that was sort of correct was to create a custom class for column sizing and alignment with the AUTO_RESIZE_OFF option set. This turned out to take up way too much programming time and I abandoned it before it was even close to working.