Is it acceptable to apply to a masters program based on your weakness, rather than you strength? As an undergrad, I took a wide variety of courses, but focused on one or two fields and took advanced courses only in those, and those fields are my strengths. I intend to do a PhD, but now I'm applying for Master's programs, and I actually want to focus on the fields that I received little to none education in my undergrad on, and the subjects that I wasn't very good at. What I want to do for my PhD is more directly related to the subjects I'm stronger at, but a knowledge in those I'm not very strong in would be significantly useful too.  

To me, that sounds totally acceptable, since I want to fill in the gaps and learn something new, rather than repeating what I already have a good knowledge on and possibly going a little deeper in it, especially as I took quite a few graduate-level courses in the fields I focused on. 

I am wondering if that's acceptable and sounds reasonable to admission committee and graduate schools too. Given that they probably have applicants who are actually applying for what they have a strong background in, would it make sense for me to compete with them with this justification that I want to improve the weaknesses in my background by throwing myself at those fields and "learn to love them", or should I just apply for what I'm stronger in and try to improve my knowledge in other fields through self studying?

(Please note that by "field", I'm actually referring to subfields within a major field. So it's not that I've done Management and I want to study Dance Performance, it's more like PDEs vs Algebra, which would mean applying to Applied Math vs Pure Math.)
Your reasoning is excellent and I would suggest you stick with this approach: All educational programs exist to increase the knowledge and skills of the student, which presupposes weakness relative to the outcome of the program.  Remember that you need to convince the admissions committee that your undergraduate record is strong enough to justify admission to the Masters program, but at the same time, it is your intention to focus on up-skilling in your areas of weakness, with a view to becoming sufficiently competent for entry to a PhD program at a later time.  There is no contradiction in these two things - your existing set of skills from your undergraduate program might legitimately be considered to be strong enough for entry to the Masters program, but weak in comparison to how you will come out (this being the entire  point of education).

In terms of assessing postgraduate applicants, this is generally the kind of student I would prefer --- one who is able to look at his/her existing skills in a realistic way, identify weaknesses, set goals for improvement, and be proactive in plugging those weaknesses to achieve goals.  Would that there were more students like this!