How does "Word Size" affect compression?

It really depends on the data you're compressing and the algorithm used.

Word size

Enter the length of words, which will be used to find identical sequences of bytes for compression. For LZMA, big word size usually gives a little bit better compression ratio and slower compression process. Big word size parameter can significantly increase compression ratio in case when files contain long identical sequences of bytes. For PPMd word size has a big meaning. It strongly affects both compression ratio and compression/decompression speed.

There are some comparisons here