Question

If the resistance r is increased , what will happen to balancing length metre bridge

Answer 1

It doesn't affect the balancing length meter bridge.

In the reasonable condition the current through the galvanometer is  zero in ideal conditions, so changing the arrangement opposition between two of the very same voltage will have no impact.  

In another case, wobbly such a change will bring down the affect-ability / sensitivity and make the balance point more earnestly toward find.