Sometimes they can, sometimes they cannot. Witness the recent description of a giant rodent from South America here.

The animal had been known from fragmentary bones for several years, but only a full skeleton gave a real idea as to its true size. However, once one has such a mile post, it makes it possible to interpret future finds of isolated bones with greater confidence. In many cases of course, one does not have a perfect parallel to the fragmentary bones. A paleontologist may find new bone fragments and identify them as "rodent" without being able to be anymore specific. However, as paleontologists gain more complete skeletons, they can compare such fragmentary remains to a range of complete rodent skeletons of various sizes and use this comparison to estimate body size. Also, aspects of bone histology (cell structure) coupled with the cross-sectional area of the bone, may give a sense of its weight-bearing capabilities.

Paleontologist use mathematical equations to figure that out. Using bones from animals they know (mice to elephants) there seems to be a direct relationship between the size of bones (say the leg, arm or rib) and the overall size of an animal.

There are several ways to estimate the size of a fossil animal. One way is to compare the found bones to the bones of an animal of known size. So, if you found a leg bone from a fossil rodent, you could compare it with a leg bone of a living rodent whose size you already know. For dinosaurs, we would compare a leg bone to that of a living reptile. However, we have to be careful of important differences such as a bipedal or quadropedal lifestyle, age, etc. to make sure that our comparison is valid.

Also, we can use clues from footprints, including the size of the foot and the probable weight of the animal; clues in their coprolites (fossil poop)that indicate what and how much an animal was eating; the size, shape, and composition of limb bones that indicate the amount of weight that the limb was bearing; and many non-limb bones preserve evidence of muscle attachments, which can help us estimate the size of muscles and the amount of weight force they exerted. Altogether, we rely a whole lot on comparisons to living animals that we understand very completely to piece together clues of how ancient extinct animals were put together.

This shows that you are thinking about how we know what we know. The bones give scientists some direct information. For example, if you put the skeleton together, and it's one meter tall, you can tell the animal was a bit taller than that because you have to add in the muscles, fat and skin.

To tell how much it weighed, you have to use what we know from other animals and apply it to the extinct one. For example, heavier animals must have thicker bones. Scientists can measure many animals for which they know both the bone thickness and the mass of the animal. When they have a lot of them, they can come up with a formula that will allow them to predict the mass even if they only know the bone thickness. They won't know the number exactly, and individual animals may have more or less fat, but they can get a good idea.

Try something like this with your friends. Measure the circumference of their head and the length of their hand. Make an X-Y or scatter plot of your results. You can use a program like Excel to make a graph and draw a trend line or you can do it by hand. Then measure just the head of some other friends and see if you can predict the size of their hand. Or measure just the hand and predict the head. Can you make a good prediction?

In living animals we know that the size of certain bones/teeth correlates very closely to the size of the entire animal. For example we can use information about the length of the thighbone (femur) in various mammals(for example a rat, elephant, cow), and the known weight of those animals, to make an educated guess about the weight of a prehistoric animal we might know only from that single bone.

We have to compare the bones to the same bones of living animals, and attempt to scale the size of the animal appropriately. It is not an exact science, and our confidence in our result is often quite poor (for instance, T. Rex probably weighed between five and nine tons - which is quite a range). It gets even more difficult when you have only a very few bones of an animal, especially if the animal has no close relatives or has clearly modified the shape of its body such that some bones are not in scale with its relatives. There, it's more of a guess, and the margin for error is larger.