Weight The Same, Body Getting Fat

What do you mean by getting fat? Are your clothes tighter, or do you just look flabbier than before?

1kg of fat takes up more space than 1kg of muscle, because it's less dense.
So two people weighing the same but with different body fat percentages will be different sizes - the person with a higher percentage of body fat will be larger.

You can shed fat through dieting alone (i.e. no exercise), but you will also reduce muscle mass, since when your body is in a calorie deficit it is fairly indiscriminate about what type of fuel it burns instead - it will burn both fat and muscle.
Cardio exercise will burn more calories and so speed up the rate of weight loss, and will improve muscle tone to a degree, but typically won't build a lot of new muscle. So someone doing this would get smaller and lighter.

The only real way to gain significant muscle is to exercise, mostly through resistance training - weights.
Coupled with a controlled diet, this is what most people find to be the best way to "recomp" their bodies (recomposition) where they get smaller but often stay the same weight/get heavier by increasing their muscle and reducing their body fat percentage.
(I've been doing this for about a year now, and am the same size I was at about 55kg, but now weigh 60kg! I'm also much stronger and more toned-looking.)

So really it depends what your objective is.
Are you happy with your weight (if you're average height, it's already towards the low end of healthy in BMI terms), but unhappy with your size?
If so, biochemistry sadly may not be on your side, and you may need to exercise to get the results you want.
All these things come down to how much you want the result versus how much you're willing to change...

You have judged yourself as lazy, that can't feel good!
It's also not going to get you the body you aspire to.

"Fashion Model, here I come!"

Speaking as an old fart - please don't take health for granted, it needs to be worked at.