It's only been a month. The weight doesn't magically drop off the minute we decide we need to lose. While a safe weekly weight loss would be 1-2 pounds, there may be weeks you don't lose. There may even be weeks when you gain ! And that doesn't mean you're doing something wrong. This is NOT the Biggest Loser. Those types of dramatic losses are just not typical.
What to do ? As the coaches all say,"Trust the process". IF you continue to eat right, watch your portions and get some regular exercise that includes some strength training, the weight will come off with time. BUT, you have to give your body time to change. You didn't gain the weight overnight. it's not coming off overnight. It really could take 6-8 weeks of healthy eating and regular exercise before a person sees a change in the scale. And that too is perfectly normal.
One thing I will recommend is that you don't do strength training here and there. Do your best to dedicate at least one workout per week to strength training. And don't be afraid to lift a weight that challenges your muscles. You will not bulk up. that's a misconception. Women don't pack on muscle the same way men do, but we both benefit from the workouts.
But, once again, you have to be patient ! Contrary to what happens on the Biggest loser and contrary to what those late night informercials say... you will not change your body in 30 days or less. That just doesn't happen in reality. Weight loss is a slow steady process that takes time. You didn't gain the weight overnight. It's not coming off overnight.
So, do make sure you're doing some strength training. And no, increasing the amount of cardio will not speed up your weight loss. that too is a misconception. Weight loss is all about what we eat. Good nutrition is what takes the weight off and keeps it off. Exercise is what keeps our bodies fit and healthy.
And you are not too old to lift a heavy weight. I'm older than you and I lift regularly. I do push ups too. You'd be surprized how strong you are if you give yourself a chance.
Patience, it's a virtue.