Let me unseasonably conclude the Christmastide series of posts on thinking with assent with a brief look at the "thinking axis" of those plots, at what might be said to increase in relation to our thinking that signifies an increase in our faith.
"Pondering" may be the best term for the sort of thinking St. Thomas has in mind here. Pondering is thinking about something in order to understand it better or more fully; in the case of a matter of belief, in which one assents to what one ponders, pondering attempts to see more clearly what can be seen, including the implications and consequences of the belief and what is involved in making room for that belief in the believer's life.
This concept of pondering is extremely subjective. It's not the sort of thing that can be compared between two people, in terms of time spent pondering or effort spent while pondering. One person may quickly understand all he ever will understand regarding a belief, while another person may spend hours in unprofitable noodling. Moreover, a person may find that different beliefs call for different amounts of pondering.
See how I snuck in talk of the "amount" of pondering? I mean pretty much what you'd think I mean: the effort put into pondering over time.
I've been a bit fast and loose on the distinction between believing, which is thinking with assent, and faith, which is the virtue of sharing God's knowledge. Believing is the interior act of faith (confessing is the exterior act), which is to say it's what you do when you engage in your habit of faith.
So if you have faith in Christ, there are a whole bunch of things you believe, but you're only actively believing at most a few of these things at any given time. (That you actively believe all of them over time means you habitually believe them, which is to say you have faith.)
With all that said, I think there's a case that the more one ponders the elements of a set of beliefs, the more faith one has.
Now, I've already pointed out the subjectivity of pondering, so we can't say that someone who spends more time pondering Christian beliefs necessarily has greater Christian faith than someone who spends less time pondering. The simple-minded saints are in no way indicted as lacking in faith by this line of thought.
Similarly, such comparisons as between the centurion, who seems to have made up his mind and gone fully into external action well before he had a chance to speak to Jesus, and the disciples, who never stop pondering and never start acting with great faith, aren't objections so much as illustrations of this subjectivity. The centurion was well-prepared to understand and accommodate his belief that Jesus could command the servant be healed, even as the disciples were still trying to graft their beliefs regarding Jesus onto their wrong opinions about what the Messiah would do.
Another objection is that certainty is more clearly essential to faith than is pondering, and certainty and pondering seem incompatible, if not contradictory. "God said it, I believe it, that settles it," as the saying goes. We can preserve St. Augustine's formula of "thinking with assent" by using a modest reading of St. Thomas, that the thinking is less a deliberating action than the state of incomplete deliberation. If you believe Jesus is both God and man, will you actually believe it any more if you chew on it for an hour or two? And if you're constantly worrying over the same belief, doesn't that suggest you don't really believe it?
Sed contra, "And Mary kept all these things, reflecting on them in her heart."
Respondeo, faith is a habit, habits involve acts, and performing the acts involved in a habit more can't be a sign of a weakening of the habit. In this case, belief is assured by assent, so thinking about it more doesn't mean you believe it less.
What happens through pondering the truths of the Faith is that they become more completely a part, eventually the focus, of your life. For the objection, I was trying to think of an example of something I believe that I don't think I need to ponder more, and I couldn't. The most basic beliefs -- God exists, Jesus is God -- reward on-going pondering; even the superficially dry "facts" of the Faith -- that Jesus went here and did that -- reveal themselves as unbounded mysteries.
Moreover, I suspect it's in some sense true that a belief you do not ponder [or confess, but that's another show], at least occasionally, is not part of the faith you hold.