Start wirh 
Dim FoundSrc As Range
Dim FoundDest as Range

Set FoundSrc = Sheet1.Rows(1).Find("Weight(kg)")
Set FoundDest = Sheet2.Rows(1).Find("Weight(kg)")
If not FoundSrc is Nothing And Not FoundDest is Nothing then
FoundDest.Offset(,1) = FoundSrc.Offset(,1)
You might have to edit the Find Parameters.