Light Grabbing is a glitch that allows grabbable objects of the heavy weight class to be grabbed light, which allows Mario to jump and run while holding them. It applies to both Chuckya and King Bob-omb, although not all method will be possible on all objects in vanilla. There exist three ways to grab an heavy object light: A water grab, a ledge grab and triggering a textbox while holding an heavy object.
When grabbing an object with a water grab, the game doesn't check for the weight of the object, the result is always a light grab. In theory, Mario is not supposed to be able to water grab Chuckya or King Bob-omb, but this can be accomplished in Wet-Dry World with precise timing.
It is possible to grab both Chuckya and King Bob-omb using an edge grab. To achieve this, Chuckya must be close to an edge and Mario must be facing in a way that he will be airborne in the first 3 frames of a punch, but that his punch will be in the object's grabbable area. When Mario starts his punch, the game will check whether he is in the correct action to grab the object in front of him and set a flag accordingly. The only valid action for an heavy object is a punch, while diving and punching are both valid actions for light object. If Mario then becomes airborne, he can dive on the first frame while the flag is still active, allowing Mario to pick up the heavy object from a dive. Since a dive cannot normally hold an heavy object, it defaults to putting Mario in the light object state.
Light Grab via Text
If Mario holds a heavy object and triggers a textbox, he will be put in the Standing with object action, effectively making the object light. This is because the cutscene action sets Mario's animation, and will always put him in the light animation, no matter the weight of the object he holds.