So to weigh = vážít + Acc?
Yep. Though the infinitive is with short i: vážit ;)
no si... ??
Nope, not for "weigh" (vážit, as opposed to vážit si).
i am wondering why not "Žofie své dítě váží " ?
'her child' could be not a Žofie's one. In such a context 'ji ditĕ' seems to be acceptable, doesn't it?
That would be "její".