In windows, program A takes up 10 MB of RAM and 27 MB of virtual memory. The RSS/Size value in Linux for program A is 37 MB. This adds up. The man page for PS in Linux says "SIZE is the virtual size of the proc (code+data+stack)". What exactly does this mean?

When a process is created in linux an area of memory is mapped for said process. The memory consists of the amount of space for the program itself (aka the code), the heap (aka the data), and the stack (where the local variables for a single procedure and return values and such get stored). This is all "virtual" address space. It is not necessarily contiguous in memory and might not reside in actual physical memory. The other thing you have to be aware of.... if a program dynamically allocates a large piece of memory and frees it you might not see an immediate reduction in the total memory usage for the process. Linux takes the "lazy" approach to freeing memory. When you free memory it makes a note that it is free but doesn't actually do anything about it until something else needs that memory.

It is hard to get more specific without going into an amount of detail you probably don't care to know.

yes many windows users come to Linux very confused about memory
often believing the resident set is the set of pages that are resident in physical memory.
this was actually true back in the day before cpus had memory manageament units i think.
It's understandable because winblows and how it works is a secret,
as jtshaw so correctly pointed out
RSS is
The total virtual memory size of the process mapped pages , including any memmapped files and/or devices being mapped to the proccess.
it is even possible for you the Linux user to increase the basic page size of your memory and insrease performance by reducing the size of the arrays actually resident in memory used to keep track of the pages themselves. You would then see larger memory use numbers and subsequent better performance.
so you just have to give up on legacy 1983 windows concepts