Archaeology and the forensic analysis of human remains can tell us a lot about the health of individuals, while not perfect bones can be used to provide solid guesses for such things as age at death, nutritional deficiencies (particularly childhood malnutrition), stresses of daily life (such as repetitive labor) and some diseases like tuberculosis. Likewise under the right conditions the analysis of soil linked to latrines can provide evidence for the nutritional intake of the population and parasite presence (for example, there has been some interesting work done on this in Pompeii).

This is all a way of saying that, theoretically, there are tools that could provide pretty illuminating answers to this question, but I am not aware of this work having been done yet (I would be thrilled to be wrong, of course). In general this sort of work on standards of living in the Roman empire is in its infancy, and getting to a level of analysis fine grained enough to distinguish specific sectors (even one as visible as the soldiery) is quite a bit of work. At the moment, probably the best sketch comes from surviving documents that let us know, for a handful of legions, for a handful of years, how many soldiers completed their service of twenty five years and were given an honorable discharge. This is pretty thin evidence to make sweeping claims, but from it we can say that the rate of mortality of soldiers was not significantly different than the civilian population. If you factor in the existence of combat mortality this may mean that soldiers were a bit less likely to die of natural causes, and thus were a bit healthier than the population as a whole, but it was probably broadly comparable.

For their physical fitness in terms of "were they swole" rather than "were they healthy" our best evidence comes from De rei militari, a military manual written by Vegetius describing the army of the early imperial period. It is problematic because it is not descriptive but rather proscriptive--in other words he is making an argument for what armies should be like based on his understanding of the early imperial army rather than something like a survey work to understand what actual military practice was. That said the book is not fantasy, and is probably a reliable guide to what can be called "docterine". And given this, the emphasis on training and exercise (taking up much of book 1) is striking. For example:

We are informed by the writings of the ancients that, among their other exercises, they had that of the post. They gave their recruits round bucklers woven with willows, twice as heavy as those used on real service, and wooden swords double the weight of the common ones. They exercised them with these at the post both morning and afternoon.

This is an invention of the greatest use, not only to soldiers, but also to gladiators. No man of either profession ever distinguished himself in the circus or field of battle, who was not perfect in this kind of exercise. Every soldier, therefore, fixed a post firmly in the ground, about the height of six feet. Against this, as against a real enemy, the recruit was exercised with the above mentioned arms, as it were with the common shield and sword, sometimes aiming At the head or face, sometimes at the sides, at others endeavoring to strike at the thighs or legs. He was instructed in what manner to advance and retire, and in short how to take every advantage of his adversary; but was thus above all particularly cautioned not to lay himself open to his antagonist while aiming his stroke at him.

This is solid exercise, particularly when combined with swimming, jumping, running, carrying heavy packs, etc that is also recommended. It is hard to know exactly how closely this training regimen was actually followed, but at the very least physical fitness was at least considered important.