It's not exactly what you're looking for, but try going to about:memory and hitt...

It's not exactly what you're looking for, but try going to about:memory and hitting Measure. It gives per object allocations:

    │  ├────6.04 MB (01.59%) -- top(https://news.ycombinator.com/item?id=8518903, id=105)
    │  │    ├──5.89 MB (01.55%) -- active/window(https://news.ycombinator.com/item?id=8518903)
    │  │    │  ├──4.64 MB (01.22%) ++ layout
    │  │    │  └──1.25 MB (00.33%) ++ (4 tiny)
    │  │    └──0.15 MB (00.04%) ++ js-zone(0x7fb875a85800)