.docx is a new file format. Basically, it’s XML, which means that, going far into the future, documents are supposed to stay readable as opposed to .doc and previous MSOffice formats, which were just 1’s and 0’s.
Because it consists of quite a few files, and because XML is quite larger than those 1’s and 0’s (when .doc was developed, hard drive space still mattered), these files are compressed into a single archive (like zip files), so it has nothing to do with the size of your document.
The reason Microsoft converted to this new format was because another, open format had been developed called OpenDocument, which includes e.g. .odt files for text documents. Microsoft likes to keep control, however, so because the industry (or actually, governments) called for an XML format like OpenDocument, they developed their own.
This new file format is technically XML, however, it is written very badly. However, it has the label “XML” so governments are happy.
So, bottom line: if you want other people to be able to open it, choose .doc, if you want these documents to be safe, install an OpenDocument plugin for MS Office or install an Office suite like OpenOffice that does supports (among others) OpenDocument.