If you read the question on almsdeeds in St. Thomas's Summa Theologica, you can construct the following model of the levels of wealth he identifies.
A preliminary note: St. Thomas assumes, perhaps even insists on, a just disparity of wealth based on station in life. I have no particular insight regarding how much of this is due to his society (highly stratified), his upbringing (as an Italian nobleman, albeit one destined for the Church), his state in life (a mendicant religious), or his temperament (he is very fond of hierarchy), as opposed to his recognition of the truth of things. I suspect, though I am no medievalist, that at least part of what St. Thomas has in mind with this is the idea that certain stations in life imply maintaining one or more households, including servants, and extending hospitality, showing noblesse oblige, and so forth; so that the idea goes beyond the lines of, "Really, lawyers' wives ought to wear cashmere."
In any case, here's the model; the ideas are St. Thomas's, the terminology is my own.
At the bottom, the least wealthy are in a state of "Physical Insufficiency." This means they don't have enough to meet their physical needs, and if they don't get something from somewhere, they're going to die soon.
Next comes "Physical Sufficiency," a state in which people have enough to keep body and soul together. They don't need help just to stay alive, but they aren't doing much better than just staying alive.
Third is "Unbecoming Adequacy." Those whose wealth is unbecomingly adequate have sufficient wealth that strangers wouldn't think of them as charity cases, but not enough to live as they ought according to their station in life.
The next stage is "Becoming Adequacy," in which people have all the wealth required to maintain them in a manner suited to their station in life. The man of becomingly adequate wealth can take care of himself and those he's responsible for, and might even have a little set aside for the predictable vicissitudes of life.
Wealth at the level of "Excessive Adequacy" is wealth that not only maintains the household in a suitable manner, but ensures against even the remote and highly improbable downturns that might come in the future.
Finally, there is simply "Surplus Wealth," greater wealth than could reasonably, or even not-so-reasonably, be required for the household.
Now, how do these levels of wealth fit into St. Thomas's conception of the virtue of almsdeeds?
For starters, he regards giving corporal alms -- material aid given to someone in need -- as a matter of precept -- meaning we are categorically bound to do it, on pain of mortal sin -- in certain circumstances. Those circumstances may have to do with the giver or with the receiver. "On the part of the giver, it must be noted that he should give of his surplus... On the part of the recipient ... we are not bound to relieve all who are in need, but only those who could not be succored if we not did succor them."
So St. Thomas teaches that all surplus wealth is to be given in alms, on pain of mortal sin, which should not surprise anyone who has ever read the Gospels. But he adds that, in determining what is surplus wealth and what isn't, the giver shouldn't "consider every case that may possibly occur in the future, for this would be to think about the morrow, which Our Lord forbade us to do, but he should judge what is superfluous and what necessary, according as things probably and generally occur." What I've called "Excessive Adequacy," then, must also be given to those in need.