The question of ponies' height has been thoroughly researched: it looks like the adult ponies are around 100 - 120 cm (3 ft. 4 in. to 4 feet) high. But how much do they weigh?
From a discussion about this exact same question on Reddit:
I'd say it kind of depends on what type of pony they are. The earth ponies are probably the heaviest, while pegasi are probably the lightest. My guesses would be:
Earth: 250-350 pounds. This is due to the fact that real life ponies typically weigh about 450 or so, and the fact that the show's characters have some differences in anatomy from real ponies. They also likely weigh more than the other races because of their earth pony strength and durability.
Unicorn: I'd guess around 175-275. They seem like they'd kind of be in the middle of the other two when it comes to weight. They don't have any reason to be heavier, nor do they have a reason to be lighter.
Pegasus: Maybe 125-225. They need to be lighter than the other races so they can carry themselves in the air. Wings aren't typically powerful enough to carry 400+ pound creatures, after all.
Of course, there are deviations to this. Bulk Biceps could maybe weigh as much as 300, and Big Mac could probably weigh up to 500 or so.
Another user on mlpforums.com went with a more scientific approach:
Judging by the fact that pegasi can fly, I'm going to guess that they aren't too heavy.
For simplicity, let's just say that RD can output one horsepower. This is equal to 746 watts of power. One watt is one joule per second, which is also:
So, to solve this, we need to know these bits of information:
How fast RD can climb. The acceleration due to gravity, which is 9.81 meters per second per second. The amount of power RD produces, which is assumed to be one horsepower.
That will leave only one variable left, which will be RD's mass.
So, I'm going to make the simple assumption that RD can ascend at a rate of one meter per second, at full power. This is equal to a speed of 3.28 feet per second, for reference. This means that RD's mass (and thus her weight) can be represented by the following equation:
746 watts = 9.81 meters per second per second * mass kilograms * 1 meter per second
Or, more simply:
746 = 9.81 * mass
This can be solved algebraically, which gives us an answer of 76 kg. This is 168 pounds.
From my own research, I have not found any official word on the subject, so this is all pure speculation. It most likely comes down to two schools of thought: realism, how it applies to our universe, or realism, as how it applies to the show's universe.