It can only be solved by temporaries/guess and check. Sometimes you have to follow the chain a long time before you reach a contradiction and have to go back. This is not the kind of puzzle that is usually played.
Fully logical, tip if you get stuck, compare the structure of the bottom two rows to see where the columns can rise on the right side, given the restriction to 1 & 2 of the column widths from the 7 on the bottom row.