I'll quote a variety of sources on the meaning of the Roman virtue gravitas which will hopefully give some indication of what the Romans meant by the term.
One definition I found on the web is this:
Gravitas is an expression used to describe a man who shows dignity, character, and a purposeful life. In roman times a male's gravitas determined when he would leave the ranks of boyhood and become a respected man.
Then there's this:
With its origins in ancient Rome, gravitas is understood to be one of the foundational virtues that men were expected to possess as part of fulfilling the proper role in society. Along with pietas and dignitas, gravitas formed the basis for the expression of all other essential virtues.
As a Latin word, gravitas is understood to embody several complementary attributes. Generally, gravitas is understood to mean dignity, duty, and seriousness. All three qualities were thought to be important in male personal deportment, and were often used as a means of determining when a boy could rightly claim to have reached his majority and could be considered a man in both psychological as well as physical stature.
Elsewhere we find gravitas defined as:
A sense of the importance of the matter at hand, responsibility and earnestness.
...the virtue known in Latin as gravitas, or gravity, a deep-rooted seriousness defines Roman character
A few thoughts spring to mind. First, if gravitas makes the Romans sound too serious, it should be remembered that they also thought of comitas as a virtue, which is defined as "ease of manner, courtesy, openness, and friendliness".
Second, the Romans saw gravitas as a distinctly masculine virtue - it was associated with the public role that adult men were ideally supposed to play in society. In other words, being a virtuous man was not only about being a good father or showing character in your personal life. Masculine virtue was expressed to a large degree in the qualities demonstrated in publicly serving your community and tradition.
Finally, the discussion of Roman virtues should be of particular interest to American conservatives. Why? Because the founding fathers are often associated with a liberal world view. But the founders were also strongly influenced, it seems, by the Roman virtues - which then injects a certain preliberal or non-liberal element into their outlook.
From one website we learn:
Cicero, the antirevolutionary orator of the first century before Christ, had an enormous influence on the Founders...The American Founders discovered not only a venerable political system in Roman tradition, but also extraordinary men whom they sought to emulate...The poet Virgil wrote of an ideal that was Rome...His writings during the time of Emperor Augustus helped to sooth the Empire after a century of civil war and recalled to the disordered Roman mind the old Roman virtues: labor, a joy and purpose in one’s work; pietas, knowledge of one’s proper relation to the higher powers inciting devotion to one’s religion and one’s country; and fatum, Rome’s duty to bring peace, order and justice to the world.
Perhaps some of the influence of the Romans was incorporated into a liberal culture, but there is much that is decidedly non-liberal (e.g. the virtue of pietas). Perhaps American traditionalists can restore a sense of those non-liberal virtues held by the American founders.
To be more specific, let's take three Roman virtues: labor, pietas and fatum. Labor is the idea that it is a manly virtue to be self-reliant. This has been, I think, part of a grass roots American culture which perhaps still lives on in the Tea Party movement. It is not the same as the modern liberal belief in individual autonomy. Liberal autonomy talks of self-determination, but in the sense of throwing off limitations on what we can choose to be. Labor does not mean stripping oneself of predetermined qualities, it means not being reliant on the state but being able to take care of oneself. Left-liberals have entirely abandoned this virtue, classical liberals less so.
Fatum was the idea that Romans were virtuous in the sense of taking on the responsibility of bringing peace and prosperity to the world. Again, there is little trace of this left in left-liberals, who believe that America brings exploitation and violence to others. But you can see a modern day version of it in certain kinds of right-liberalism (e.g. neoconservatism) in which it is believed that there is an American exceptionalism involving America bringing democracy to the world (or being a light on the hill).
So the first two Roman virtues, labor and fatum, are embedded to some degree in certain kinds of classical/right-liberalism but are absent within left-liberalism. But the third virtue, pietas, is found in neither. It is a more specifically traditionalist virtue. It includes a sense of duty and connection to your ancestors, to your family and to your own people.
Below is a YouTube video by Dr Shanon Brooks, who is calling for Americans to "revalue" themselves. I have to say that I think "fatum" as expressed in the idea of "manifest destiny" has not served America well and I can understand why some Americans have reacted against it. I don't think it's a good virtue for Americans to "revalue" themselves with. But it is to the credit of Dr Brooks that he includes pietas in his list of virtues which helped to make America. He is not ignoring the more traditionalist virtue that was present in the American founding: