Quatrain 2 Summary

Get out the microscope, because we’re going through this poem line-by-line.

Now proud as an enjoyer, and anon

This line is a little tricky, because it isn't immediately clear what Shakespeare is talking about. Actually, he isn't talking about a "what," but a "who"—the "miser" that we learned about back in Line 4. In Line 4, we heard that this miser found himself in a certain state of "strife." Now, Shakespeare is explaining what that state of strife is like.
First of all ("now"), the miser is "proud." Why? Because he's an "enjoyer" of (i.e., someone who gets to enjoy) his wealth.
But will he always be so lucky? The line makes this seem a little doubtful, by ending with the word "anon," which means "immediately" or "straightaway." As you can see, by ending the line with a phrase meaning "and immediately," Shakespeare has once again left us—and our new acquaintance, the miser—in suspense. This makes sense because he still hasn't really explained how a miser finds himself in a state of "strife."

Doubting the filching age will steal his treasure;

Aha! Now we get it. Or, we would if there weren't some tricky words here that don't make sense. First important translation: in this context, "Doubting" is being used in the old-fashioned meaning of "fearing." Second important translation: "filching" means "stealing." Finally, by the "age," the speaker means the times in which the miser is living.
So, in other words, the miser is "Fearing that the stealing age will steal his treasure," which is, you know, a pretty reasonable thing for a "stealing age" to do.
Is the "strife" of the miser clear now? From Lines 5 and 6, it looks like the trouble is he doesn't know what he wants. One moment, he's totally content, enjoying his possessions (his wealth); but then the next moment ("anon"), he can't enjoy it, because he's afraid someone will steal it.
Or he's afraid something will steal it. If you think about it another way, age is the best thief around, eventually robbing us of everything (our sight, our movement), even life. To suggest that age is a thief is to use personification. After all, age is an abstract concept, and can't really rob us the way some guy with a mask and a dollar sign on a sack can.
As we know from Line 4, this miser imagery is supposed to illustrate the speaker's own experience with his beloved. In other words, the miser is a metaphor for the speaker. How do you think their experiences might match up? While you think about that, let's keep reading to see if the Shakes-man himself sheds any light on it.

Now counting best to be with you alone,

What's going on here? Is the speaker just giving us more of the same miser imagery as before? It sure looks like it at first. After all, there are many ways that Shakespeare could have chosen to phrase the idea that appears here, which is basically, "now considering being with you alone as the best thing in the world." By using the word "counting," however, he definitely creates an image of a "miser"—of somebody counting up the coins in the hoard.
But look again. This miser or miser-like person, whoever he or she may be, is "counting best" to be with "you." But isn't "you" the person that the speaker of this poem is talking to?
It looks like, through some weird sleight-of-hand that would be the envy of Las Vegas, Shakespeare has made the speaker switch from talking about the miser to talking about himself (and his beloved). What's he going to do next, pull a rabbit out of a hat?

Then bettered that the world may see my pleasure;

Well, maybe he does pull a rabbit out of a hat—metaphorically speaking, that is. That's because the speaker is describing a change of heart. Back in Line 7, he was all about keeping his relationship secret, so that he could have it all to himself. In Line 8, however, he takes a different attitude: he wants everyone to see how happy he is.
Note that the word "bettered" at the beginning of this line is carrying over the "counting" metaphor from Line 7.
Back in Line 7, the speaker imagines that he's tallied up the pros and cons and decided that the "best" thing is "to be with you alone." By saying that he has been "bettered," he makes it sound like he went back, revised his calculations, and realized that he'd forgotten to carry a one or something.
This imagery, which compares decisions of love to accounting, seems designed to remind us of the miser imagery from earlier in the poem. Why do you think Shakespeare chose to make the speaker represent himself in this way?