I'm not sure why you think that a research statement should be 1-2 pages. The length of a research statement depends both on the academic field and (to a lesser extent) on the type of institution one is applying to. In my experience, when a research statement that is only 1-2 pages long is desired, the position posting will mention that explicitly, often using slightly different language ("research summary").
In my field -- mathematics -- if a length of 1-2 pages is not explicitly asked for, then 1-2 pages would be distressingly short, to the extent of jeopardizing your chances. I would put 4-6 pages as a more reasonable range for those applying for junior faculty positions. (More senior people can submit longer statements, but after a point people will stop reading.)
To be specific, I have been closely involved with the job search of two junior colleagues, in mathematics. Both are interested in finding a "faculty position that emphasizes both research and undergraduate teaching." Each of their research statements was about 4 pages plus references. They have each done very well on the job market -- on-campus interviews from both large universities and top liberal arts colleges, and one already has a good job offer. I would not want any student, mentee or junior colleague of mine to send out a 1-2 page research statement until they convinced me that this length was specifically wanted by the institution they're applying to.
My question is: would it be an issue if the lengths of the 2 documents are significantly different?
In my experience -- which is centered at a math department at a state research university -- research statements are generally 2-3 times longer than teaching statements. The only teaching statement I've ever seen that was approximately the same length as a research statement was my own. (Regular readers of this site will be shocked to learn that I can be seduced by the sound of my own written voice. Only over long years and after reading, writing and refereeing many technical papers have I come to a halfway decent appreciation of the virtues of brevity.)
My question is: would it be an issue if the lengths of the 2 documents are significantly different? For example, if my teaching statement is 2 pages but my research statement is only 1 page.
To me, someone whose teaching statement is twice as long as their research statement is signalling in the strongest possible terms that they are more interested in teaching than research...i.e., up to the point where they may not be doing much post-PhD research at all. But again: please check on your local academic culture.
Will a hiring committee automatically view this as the candidate being unbalanced?
Not automatically, no.
In other words, does disparity in length between the two documents outweigh the content of the documents?
No, the content is most important. If in your one page research statement you give a clear description of very strong research, people who were expecting a much longer document will think "What a short research statement. That's weird. But it sounds good -- let me check the CV / publication list / candidate's webpage for more details."
Added: I'm finding some evidence online pointing to the possibility that research statements in mathematics may be longer than in many other academic fields:
- This source advises that research statements in CS should be 2-3 pages.
- This source suggests that research statements should be 1-2 pages. Upon questioning, it becomes clear that the advice is scoped only for the humanities.
Anyway, you should definitely not choose the length of your research statement by what some internet academic tells you! You should do so by (i) talking to your thesis advisor about it and (ii) comparing notes with others who are or recently were on the job market. Getting a look at application materials of those who recently got the type of job that you want is ideal. That's what friends are for.