rsync delta-transfer algorithm does this by default. Quoting rsync manpage:
DESCRIPTION
Rsync is a fast and extraordinarily versatile file copying tool. It
can copy locally, to/from another host over any remote shell, or
to/from a remote rsync daemon. It offers a large number of options
that control every aspect of its behavior and permit very flexible
specification of the set of files to be copied. It is famous for its
delta-transfer algorithm, which reduces the amount of data sent over
the network by sending only the differences between the source files
and the existing files in the destination. Rsync is widely used for
backups and mirroring and as an improved copy command for everyday
use.
If you want to disable it, you will have to use the -W or --whole-file option.
-W, --whole-file
This option disables rsync's delta-transfer algorithm, which causes all transferred files to be sent whole. The
transfer may be faster if this option is used when the bandwidth
between the source and destination machines is higher than the
bandwidth to disk (especially when the "disk" is actually a networked
filesystem). This is the default when both the source and destination
are specified as local paths, but only if no batch-writing option is
in effect.
If you really know how much your file have changed doing, you could even optimize this delta transfer behavior by tunning your delta block size:
-B, --block-size=BLOCKSIZE
This forces the block size used in rsync's delta-transfer algorithm to a fixed value. It is normally selected
based on the size of each file being updated. See the technical report
for details.
And if you want more information about the algorithm itself, you can find it here: The Rsync algorithm
rsyncbehaves this way by default. As long as the minor change is a minor change to the file, and the file already exists on both sides of the link in near-identical versions, the data transferred should be much less than the total file size. From the first paragraph in the man page: "It is famous for its delta-transfer algorithm, which reduces the amount of data sent over the network by sending only the differences between the source files and the existing files in the destination."