No, different elements cannot have the same atomic weight. Atomic weight, also known as atomic mass, is a specific property of each element and refers to the average mass of all the naturally occurring isotopes of that element. Isotopes of an element have the same number of protons but different numbers of neutrons.
Since atomic weight is determined by the weighted average of all the isotopes, different elements will have different atomic weights because they have different numbers of protons, which uniquely define each element. For example, the atomic weight of hydrogen is approximately 1.008 atomic mass units (amu), while the atomic weight of helium is approximately 4.0026 amu. These values are distinct and allow us to differentiate between different elements.