Here are my top picks for anime like Heavy Object. Keep in mind the list is in no particular order. Enjoy the recommendations!
In 1972, the Apollo 17 mission discovered a hypergate to Mars on the surface of the moon. Soon a war breaks out between Earth and Mars, and Martian soldiers begin to descend from the sky, riding steel giants, intent on exterminating humanity.
In the year 2015, the Angels, huge, tremendously powerful, alien war machines, appear in Tokyo for the second time. The only hope for Mankind’s survival lies in the Evangelion, a humanoid fighting machine developed by NERV, a special United Nations agency. Capable of withstanding anything the Angels can dish out, the Evangelion’s one drawback lies in the limited number of people able to pilot them. Only a handful of teenagers, all born fourteen years ago, nine months after the Angels first appeared, are able to interface with the Evangelion. One such teenager is Shinji Ikari, whose father heads the NERV team that developed and maintains the Evangelion. Thrust into a maelstrom of battle and events that he does not understand, Shinji is forced to plumb the depths of his own inner resources for the courage and strength to not only fight, but to survive, or risk losing everything. (Source: AniDB)
In the crime-ridden, mafia-governed city of Ergastulum, Worick and Nicolas are two “handymen” known as “Benriya” who would take any dirty job from either police or mafia — for a good price. After an assignment from police the two met and later joined by Alex, a former prostitute who got interested in the mysterious background of the team, in particular of Nicolas’ abilities.
On August 10th of the year 2010 the Holy Empire of Britannia began a campaign of conquest, its sights set on Japan. Operations were completed in one month thanks to Britannia’s deployment of new mobile humanoid armor vehicles dubbed Knightmare Frames. Japan’s rights and identity were stripped away, the once proud nation now referred to as Area 11. Its citizens, Elevens, are forced to scratch out a living while the Britannian aristocracy lives comfortably within their settlements. Pockets of resistance appear throughout Area 11, working towards independence for Japan.
Lelouch, an exiled Imperial Prince of Britannia posing as a student, finds himself in the heart of the ongoing conflict for the island nation. Through a chance meeting with a mysterious girl named C.C., Lelouch gains his Geass, the power of the king. Now endowed with absolute dominance over any person, Lelouch may finally realize his goal of bringing down Britannia from within! (Source: Bandai Entertainment)
Renton Thurston is a 14-year-old boy who lived with his mechanic grandfather in a backwater town. Every day he dreamed of being with the mercenary “Light Finding Operation (LFO)” aircraft pilot group “Gekkostate” and riding “Trapar” particle waves—a sport called “reffing”—with their charismatic leader Holland, especially when faced with his father’s acclaimed past or his grandfather’s desire to protect him. When a young girl named Eureka riding the original LFO, the “Nirvash typeZERO,” asks his grandfather for a tune-up, she inadvertently brings the attention of the military to the garage; as a result, the garage is destroyed and Renton is forced to deliver a new type of interface—the “Amita Drive”—to the Nirvash. After a heated fight in which the Nirvash destroys the military LFOs by unleashing an immense amount of power, Renton is invited into Gekkostate. However, he quickly realizes that behind the facade of a traveling group of mercenaries is a very bitter reality.
In a faraway future, mankind lives underground in huge caves, unknowing of a world above with a sky and stars. In the small village of Jiha, Simon, a shy boy who works as a digger discovers a strange glowing object during excavation. The enterprising Kamina, a young man with a pair of rakish sunglasses and the passion of a fiery sun, befriends Simon and forms a small band of brothers, the Gurren Brigade, to escape the village and break through the ceiling of the cave to reach the surface, which few believe exist.
The village elder won’t hear of such foolishness and punishes the Brigade. However, when disaster strikes from the world above and the entire village is in jeopardy, it’s up to Simon, Kamina, a girl with a big gun named Yoko, and the small yet sturdy robot, Lagann, to save the day. The new friends journey to the world above and find that the surface is a harsh battlefield, and it’s up to them to fight back against the rampaging Beastmen to turn the tide in the humans’ favor! Pierce the heavens, Gurren Lagann!
In the year 2012 Japan was invaded by the Mu. Human-like beings from another dimension with blue blood. In the year 2015 Tokyo is attacked by invaders, who are repelled by a humanoid weapon called a Dolem. During the chaos, Ayato Kamina meets Reika Mishima, a classmate.
During that same day, he is attacked by government officials but a woman named Haruka comes to his rescue, informing him that she was sent to get him by the Organization TERRA, and that Tokyo had been sealed in a time rift where time flows one third as fast as the outside world. He flees from Haruka onto a train where he sees Reika once more. Arriving at the Room of Rah, he follows her to a tremendous egg where the Dolem RahXephon is hatched from, and upon her singing his mother appears atop the Dolem that had stopped the TERRA Invasion. In the battle Ayato’s mother is injured, and Ayato flees Tokyo Jupiter with Haruka upon seeing his mother’s blue blood.
During a summer camp, 15 children, 8 males and 7 females, find a grotto by the sea. Deep within they discover working computers and some electronic equipment, and later the owner, a man called Kokopelli. Kokopelli claimed to be a programmer working on a brand new game, in which a large robot has to defend the Earth against alien invasions. He persuades the children to test the game and sign a contract. All but one of them sign, barely a moment later they mysteriously awaken on the shore believing what happened was just a dream.
References: Wiki, MyAnimeList, ANN