Is referring to a textbook solution considered academic dishonesty? There are weekly homework assignments based on a textbook. We will finish each problem set and hand that in every two weeks. 

Since the assignments are straight out of the textbook, it is very easy to get a copy of the textbook solution manual from online sources. 

As an undergraduate student, if I try the problem myself, and then refer to the solution manual only for comparing the final answers, am I committed of academic dishonesty?

Since I have referred to the solution manual, it is very likely that I will receive a good score on the assignment. If I also have a very good score on the exam, does my score reflect that my homework wasn't copied from the solution manual?

The homework is only worth 10% of the overall grade.
I agree (as usual) with @ff524.  Consulting an outside source is not academic dishonesty in a global sense -- academic culture does not prohibit students and faculty from reading academic sources! -- but it may be academic dishonesty in a local sense: i.e., it may be against the rules of your course as set up by your instructor.  You can find out whether you are being "locally academically dishonest" in this way by consulting your instructor.

Two further points:

1) Since the homework grade is only 10%, unless the homework is wildly more difficult than the rest of the course, a student who consults answer books to do their homework is unlikely to gain a competitive advantage against other students.  In fact, as you hint at, it is more likely that such a student would miss the learning opportunity the homework is designed to provide and this would show up in lower exam scores.  The old chestnut "You would only be cheating yourself" seems to apply here.

2) Although consulting an outside source is not academic dishonesty, as ff524 brings up there is still the question of what happens after you consult it.  If you do the problem, then look at the textbook, then change the answer if it doesn't match, and never mention that you consulted the textbook, then yes, you are at least in danger of having committed plagiarism.  

Overall, you should talk to your instructor and find out whether it is permissible to consult the textbook.  If it isn't, then obviously you shouldn't do it.  If it is, then it really is and you should mention in your homework when you do so.  To an undergraduate student this practice may seem strange, but it is really the right thing to do and I would expect your graders and instructors to react well to it.