If you insist on increasing the weight, you will start to become more bulky, more weight takes more muscle mass to lift. To avoid it, just stay with lower weights and do more reps. That way you will tone the muscles but not significantly add to their mass.
Do cardio as well. I lost 200 lbs and wanted to be fit but not bulky type muscles. I did an hour of cardio after an hour of weights. Was thing, strong, fit and not those Weider type muscles!
not too much more, but more reps, twice that of a muscle builder.
If I remember right, many repetitions with light weights will increase your strength but not bulk up your muscles much, but a few repetitions with heavy weights will add bulk.