Which "Big Bertha" are you referring to? If you mean the 42 cm Siege Howitzer used at Liege in 1914, then there were plenty of similar pieces used in WWI. The British had their 9.2 inch pieces, and their 15 inch howitzer. The French had 37 cm and 40 cm pieces, as well as two 52 cm Howitzers that never saw action. The Austro-Hungarians had a small number of their own 42 cm guns, as well as their formidable Skoda 30.5 cm M1911 Siege Mortars.

If you mean the Paris Gun, then no. The Germans seem to have been the only country in WWI to have developed a 'super-heavy' artillery piece of that type. However, the French did experiment with artillery pieces of that type after WWI, though these experiments seem to have been discontinued due to the potential 'concerns' of the British. More info [here] (http://www.landships.info/landships/artillery_articles.html#)

It really depends on what your definition of a 'super weapon' is. To me, a 'super weapon' uses a new technology, or a new synthesis of old technology, in an attempt to alter the strategic situation. The V2, or the atomic bomb, are excellent examples of this. As /u/DuxBelisarius points out, the 42cm siege howitzer 'Big Bertha' doesn't exactly fit into this definition, while the Paris Gun might. Other possible 'super weapons' are the chemical weapons, and the tank, neither of which I'm particularly comfortable discussing in depth. One that I am comfortable discussing is the British work on the aircraft carrier.

Initially, the British saw the aircraft carrier as a way of providing intelligence and reconnaissance for the fleet. They were operating seaplanes throughout the war, using them repeatedly for scouting and spotting the fall of gunfire. However, they needed aircraft for more than that. The German navy didn't have enough cruisers, so attempted to counteract this using Zeppelin airships. These posed a threat to the ability of the RN to achieve tactical surprise, and had no easy counter. They could also be used for bombing. While the British attempted to use aircraft to attack the Zeppelin bases, this was ineffective - the first naval air raid, on Christmas Day 1914, was against the Zeppelin base at Cuxhaven, but little damage was done. Instead, the RN's Air Department pressed for ships capable of carrying fighters to shoot down the Zeppelins. In 1915, experiments were carried out with launching landplanes from the seaplane carrier Vindex. These demonstrated the feasibility of the concept. A few months later, in February 1916, experiments with arrester gear were carried out, showing that it might be possible to land an aircraft on a ship. This led to the decision to convert an Italian liner, under construction in Britain (but halted due to the war) to the carrier Argus. The large light cruiser Furious would receive a flying off deck replacing her forward turret in August 1917. After early trials, it was decided to replace her after turret with a landing deck. Work on this was completed by March 1918. While she was being worked on, David Beatty, the commander of the British Grand Fleet produced a plan to destroy the German High Seas Fleet in port, using torpedo bombers. This was triggered by the fact that the Sopwith Cuckoo, the first truly effective torpedo bomber, was entering production, making such a plan feasible. This attack, the first plan for which was submitted in September 1917, required 120 bombers flying from 8 carriers. However, this plan would be quashed by the Admiralty. It was revived on a smaller scale towards the end of 1918, by which time Argus and the converted cruiser Cavendish ( a light cruiser with a flight deck built over her upperworks, later renamed Vindictive) had entered service. This new plan was brought to nothing by the end of the war, but how close it came to completion can be seen in the card sent at Christmas 1918 by the officers of the RAF's torpedo bomber unit. It had a picture of the High Seas Fleet, along with the words 'Oh, that we might have met'. The RN continued its carrier experiments post-war, as did other navies. Within 20 years, the carrier had become the most significant class of naval vessel.

Others have already mentioned poison gas, Zeppelins, tanks and aircraft carriers. All were deployed in crude forms during World War One. Tanks and aircraft carriers were refined and used extensively during World War II. There was one weapon system that the US Army Air Corps tried to develop during World War One, but could not get it out of the prototype phase and actually deploy it during the war. This was unmanned aerial drones. Specifically, the "Self-flying Aerial Torpedo", which came from the fertile mind of Charles Kettering, an engineering genius who did most of his work for the General Motors corporation. The first example flew in the summer of 1918, but there were numerous problems, making the thing work right. Less than fifty were built by 11/11/1918 and none of them were shipped to France. This was a weapon that was seventy-five years ahead of its time.
Source: http://www.smithsonianmag.com/arts-culture/unmanned-drones-have-been-around-since-world-war-I-16055939/?no-ist