is surely too hard for you. Also,
As I understand Economics, researchers should do DSGE models with a deep degree of formalization. I don't approve DSGE with Dynare.
Can a person with a weak background in math

Yes you can OP, I did it myself. It will take you a lot more time and effort but you can do it. Also, it might be helpful to go through a book on how to prove things, the logical forms, since as it was referred in another comment Real Analysis is basically more about knowing how to work with logical forms of math sentences.

Thank you very much.
Is this a good reference on how to prove things?
http://webpages.csus.edu/Jay.Cummings/Books.html
Yes you can OP, I did it myself. It will take you a lot more time and effort but you can do it. Also, it might be helpful to go through a book on how to prove things, the logical forms, since as it was referred in another comment Real Analysis is basically more about knowing how to work with logical forms of math sentences.

I intend to specialize in macroeconomics, primarily in DSGE models, along the same lines of Larry Christiano
https://faculty.wcas.northwestern.edu/~lchrist/course/AEA_2018/syllabus.htmlYes but to what end?
Not a rhetorical question, what's your end goal?
Ljl.
Maybe focus on understanding economics first OP. Try some micro. Will help you out a lot more in your goal. 
What do you mean?
Studying math is said to be beneficial for its own sake.
And also math = micro = macroI intend to specialize in macroeconomics, primarily in DSGE models, along the same lines of Larry Christiano
https://faculty.wcas.northwestern.edu/~lchrist/course/AEA_2018/syllabus.htmlYes but to what end?
Not a rhetorical question, what's your end goal?
Ljl.
Maybe focus on understanding economics first OP. Try some micro. Will help you out a lot more in your goal.