Slight paradigm shift:
- Weightlifting is to build and/or maintain muscle mass.
- Cardio is added activity level i.e. extra energy output. A person will not burn fat without a calorie deficit regardless of how much cardio they do. Cardio just adds to the amount of calories one uses throughout the day. (It also improves your health in a variety of ways other than fat loss but nobody seems to care about that).
Someone gets a "skinny fat" physique when they have very low muscle mass with average, slightly below average fat mass. That person may also have a genetic tendency to carry fat mass on their midsection rather than dispersed around their body.
To lose fat, you need to eat in a calorie deficit. If you are not losing fat, then you are not in a deficit. The problem is, people in a deficit also have a tendency to lose muscle mass depending on the severity of the deficit. People will lose muscle mass down to the point where they only have the muscle mass they need to go about their daily life.
People who weightlift need more muscle mass than people who don't, so they will maintain/lose very little compared to someone who does not. In certain circumstances, it is possible to gain muscle mass in a slight deficit as well, especially for people who do not have a lot of muscle mass to begin with. So they will lose fat mass while keeping muscle mass and as a result look more "defined".
People who only do cardio while in a calorie deficit will lose muscle and fat at the same time. As a result they become smaller and eventually hit that "skinnyfat" look. If they keep going, they'll eventually reach a point where they are maintaining their muscle mass and they'll keep losing fat mass and become "skinny". Most people don't go beyond the "skinnyfat" phase because, well, excessive dieting sucks.
So it's not that cardio limits fat burning. It's that weightlifting limits muscle burning.
As another note, the more muscle mass you have, the more "toned" you'll look with higher bodyfat percentage. Meaning, if two people with the same height and bodyfat percentage but one person has 20 lbs. more muscle than the other, the heavier person will look a lot leaner than the other one. So people with low muscle mass will typically not look very lean until they get in to really low bodyfat percentage numbers.