Wemmick is an interesting character for a couple of reasons, or, more correctly, because there are a couple of Wemmicks. The Wemmick who works for Mr. Jaggers is a bill collector, whose success and livelihood depends on extracting money from people who probably don't have much--or any. As such, he has constructed for himself a cold-hearted persona with ample psychological walls to protect himself from unpleasant feelings that may arise when he is conducting his unpleasant responsibilities. His home is a sort of reproduction castle, complete with moat and drawbridge, which he has created to be a sanctuary from the less than fulfilling nature of his employment, telling Pip once that "The office is one thing and private life is another". Ironically enough, despite his efforts to separate work from home, Wemmick's finances aren't all that different from those of the people he harasses for payment, and it is this situation that probably accounts for his obsession with "portable property". Although in his personal life, he can be quite a pleasant man, as Pip observes once, "There were twin Wemmicks and this was the wrong one". One of the more despicable things the "wrong" Wemmick does is visit prisoners who have been condemned to die and arranges to receive their "portable property" as they clearly won't be needing it themselves; however, he sees this as a way of fending off financial ruin, which is always lurking just around the corner.
Wemmick tries to share the necessity of this philosophy with Pip, advising him to get a hold of as much of Magwitch's "portable property" as he can; Pip disregards this directive however, and notices how much better he feels once he has returned an item that belonged to Magwitch to Magwitch himself.
It is interesting to note that Dickens himself was no stranger to the difficulties of financial strife; his father was imprisoned for debt when Dickens was about twelve, and the youngster was forced to go to work in a blacking factory to assure the family's survival. This was also a time in England when there was a widening divide between the affluent and the poor, and the issue of money and how it can become a great negative in someone's life is present not just in Great Expectations, but also in the well-known Dickens novel A Christmas Carol.
These words of Wemmick's from Chapter XXIV of Great Expectations are said to Pip after his asking Wemmick about the strange casts on a shelf in the office of Mr. Jaggers. Later in the narrative in Chapter XXXVI,now that he has come into five hundred pounds,Pip asks Wemmick for advice about helping his good friend Herbert Pocket. When Pip tells Wemmick that he wishes to patronize his friend Herbert, who is meeting with little success in the "commercial life" by giving him money to help him, Wemmick shakes his head,
"Choose your bridge, Mr. Pip,” returned Wemmick, “and take a walk upon your bridge, and pitch your money into the Thames over the centre arch of your bridge, and you know the end of it. Serve a friend with it, and you may know the end of it too—but it's a less pleasant and profitable end.”
Then, Wemmick explains that this pragmatic approach is his opinion during the day while he works for Mr. Jaggers. At his home in Walworth, he explains,
"My Walworth sentiments must be taken at Walworth; none but my official sentiments can be taken in this office.
Later, Pip receives a letter from Wemmick.
In it, Wemmick invites Pip to Walworth where he informs Pip that Clarriker has considered taking Herbert into his business and eventually making him a partner in exchange for 250 pounds and other regular payments from Pip. Clearly, Wemmick is pragmatic in all but matters of the heart where he demonstrates a most romantic disposition. His "post-office" mouth and severe demeanor are his defense in the cruel world of Mr. Jaggers only.