How can I sustain an argument if I must also consider both sides to the question?

Although, of course, it is of great importance that your essay reflects both the (or sometimes multiple) conflicting arguments invited by the question, this does not mean the answerer has to confuse their case by supporting the weaker contentions. My personal strategy has somewhat solved this, leading to my 97% score in A Level History. The first thing to do when juggling these objectives is to confidently set out your own argument in the introduction, whilst referencing the other, weaker arguments which do have some merit. After this, you should open with your own argument, for example a paragraph arguing the successes of the Royal Navy in the years 1793-1805 were largely due to Nelson's leadership, before turning your attention to the other factors (for instance, in this case, British naval technology or French failings, etc). As you progressively consider the other factors, you should conclude each paragraph with a partial dismissal of the weaker argument; i.e., why it is still secondary to the argument you have chosen to support. Of course, you'll sum it all up in your conclusion; re-stating the superior argument, and summarising it's primacy over other factors. I find this technique provides for the most sustained and probing answers.