Wild guess, 200-300 tons.
It's a railroad bridge, and it's had 116 years of locomotives and freight cars crossing it. Freight cars are heavier and trains are faster than they were when it was built--there's a lot of railroad trusses that didn't last half that long, especially if it's a mainline bridge.
Yeah, quite sad. There are plenty of bridges that are collapsing on themselves from neglect - and here's one that is sound enough it's removed in one piece.
On a side note, any idea approximately how much a bridge like that might weigh?
This is so stupid. They hauled the bridge away IN ONE PIECE! How hard would it be to simply set it down in a park somewhere? http://www.kcrg.com/news/local/Dubuque-Loses-Historic-Bridge-168057216.html