When we talk about how heavy a metal is, we're really talking about how dense it is. Density is a measure of how tightly packed matter is. The density of a material is mass per unit volume. Density is measured in kilograms per cubic meter (kg/m3) or grams per cubic cm (g/cm3).

In summary:

He osmium and the iridium are the densest metals in the worldbut relative atomic mass is another way to measure "weight." The heaviest metals in terms of relative atomic mass they are the plutonium and the uranium.

The densest metals

Osmium and iridium are the densest metals.In other words, its atoms clump together more tightly in solid form than other metals. With a density of 22.6 g/cm3 and 22.4 g/cm3 respectively, osmium and iridium are approximately twice as dense as lead, which has a density of 11.3 g/cm3. Osmium and iridium were discovered by the chemist English Smithson Tennant in 1803.

Heaviest metal by relative atomic mass

The heaviest natural element is plutonium (atomic number 94, relative atomic mass 244.0). Other heavy metals in terms of relative atomic mass are uranium (atomic number 92, relative atomic mass 238.0289), radium (atomic number 88, relative atomic mass 226.0254), and radon (atomic number 86, relative atomic mass 222.0).

References:

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3113373/
https://scienceline.ucsb.edu/getkey.php?key=2687