The short answer is that yes, an item does in fact weigh more when it is heated. Will you ever be able to actually tell if such is the case? No. The change in weight is so infinitesimal that detecting it with just our five senses is impossible. How then, do we know that it takes place?
When studying matter and its properties, one very interesting question comes to mind. If we were to heat an object, would there be any change in its weight? And if so, would that change be reversed if the object is cooled? It is common knowledge of course that mass and weight are two very different things. Yet, there is a degree of correlation between them. And if mass were to be affected by a change in temperature, logically, a change in its weight would follow.
When two objects of the same mass and weight are weighed side by side at the same temperatures they will of course, weigh the same. Then, if one of these objects is heated, it will contain more energy than the unheated object. This is because at higher temperatures, atoms vibrate faster. This principle is also why electric current faces resistance in a heated wire.
To understand why more energy means more weight, we need to learn about the term “stress energy tensor”. In simple words, the stress energy tensor includes the mass of an object as well as its kinetic energy. Gravitational force depends on the stress energy tensor. Thus, when the object has more kinetic energy because of the excited atoms, the stress energy tensor of the object is affected as well. And so, the gravitational pull is affected and the object weighs ever so slightly more. This then also means that an object will weigh less if it is cooled down.