You are adding the tablesorter four times for both tables, hence the sorting occurs four times.
Try calling $(document).ready()
only once:
$(document).ready(function()
{
$("#newsTable").tablesorter(
{
widthFixed: true,
widgets: ['zebra'],
sortList: [[1,0]]
}).tablesorterPager(
{
container: $("#pager1"),
size: 5
});
$("#eventsTable").tablesorter(
{
widthFixed: true,
widgets: ['zebra'],
sortList: [[1,0]]
}).tablesorterPager(
{
container: $("#pager2"),
size: 5
});
});