Here's an interesting limit, which doesn't depend on things like gravity:

If I were to, say, double your height, while keeping your proportions the same, then you would end up being 8 times as heavy as you now are. That's because you'd be twice as tall, twice as wide, and twice as thick, 222 = 8. But you'd only have about 4 times as much surface area. That's less obvious for a weird shape like a human, so let's just assume you're a sphere for now (I'm a physicist by training, so most things are either points or spheres in my world...). In the spherical case, surface area = 4 * pi * r² and volume = 4/3 * pi * r^3. So, doubling r causes volume to go up by a factor of r³ = 8 and surface area by r² = 4. This is generally known as the "surface area volume law."

Okay, so who cares? Well, some things depend mostly on volume, and some depend mostly on surface area. For example, it's fairly reasonable to assume that with 8 times as much mass, you would burn 8 times as much fuel (since you have 8 times the mass of hungry cells). But the amount of heat you can dissipate into the environment depends mostly on the amount of skin area you have. So, as you get bigger, the ratio of the amount of heat you generate to the surface area with which to dissipate it grows. That means that as you get bigger, if your metabolism stays constant, you'll get hotter and hotter. So, since elephants don't generally run at 200 degrees Fahrenheit, you can conclude that metabolism has to be lower in large animals than small ones, simply because an elephant that burned fuel at the same rate (per unit mass) as a mouse would overheat and die.

Of course, the amount of heat you emit into the environment also depends on the external temperature, but, nonetheless, things like surface area/volume do give us some insights into the way things are likely to work out for a given set of conditions.