it was a role that I've already applied to.
Unless you have a prior communication with the recruiter, and the recruiter with the company, before you applied to this position, I don't see a way of the recruiter benefitting from your candidature. This is because a recruiter gets paid once you are selected, and even if you get through, the company can always reject the recruiter's claim since you had applied with them directly.
Recruiter still wants to represent me, and tells it would give a better chance for hire
The recruiter is right about this aspect. If a company has a direct relation with a recruiter, there are more odds of him being able to work the system for your interview than you relying on the cogs to turn on their own.
However this is correct only if you haven't heard back from the company, there is no point in opening 2 channels of communication with the same company.
So, in essence, you should look after your own interests and let the recruiter judge their own. As long as you land the offer and all goes well, don't think too much about it.
Source: Real life. This once happened to a novice recruiter who helped one of my coworkers land a job, and the company denied the recruiter's claims because they had an email where the coworker had sent their resume directly to the company's email id before they received it from the recruiter.
PS: As suggested in comments and other answers, there can be negative effects as well, so take a call considering all aspect.