From the Super Mario Wiki
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Mega Guys, also known as Mega Shy Guys, are Shy Guys that are fatter and bigger than normal. They first appear in Super Mario Advance, where they provide a Small Heart when they are thrown at the ground or defeated.
Mega Guys appeared in early trailer of Yoshi's Story, though they are not present in the final game. They also appear in the Yoshi Demo, where stomping one would turn it into a regular Shy Guy. A giant robotic Shy Guy appears in Yoshi's Island DS. One also appears in the WarioWare: D.I.Y. Showcase microgame Mario Adv.
In the small short that concludes the chapter in volume 26 of Super Mario-Kun, a Mega Guy attacks Mario, Goombario, and Kooper. It then pits Mario against Robirdo. Mario, however, grabs the Mega Guy and throws it against the Robirdo, defeating Robirdo and the Mega Guy.
Mega Guys also appear in Yoshi's New Island. Here, Yoshi can swallow them to turn them into Mega Eggdozers, which can be used to destroy otherwise indestructible obstacles. Mega Guys require a bit more effort than normal to swallow, as the player has to rapidly press to do it. A metallic subspecies known as Metal Guys also appear, which are used to make Metal Eggdozers.