Negotiating your salary shows your employer that you are capable, confident and comfortable with what you have to offer. Those skills are the ones your employer will value when it comes to increasing your level of responsibility, trusting you with clients and promoting you.
Hiring managers expect you to negotiate and some will think less of you if you don't. The chances of you being seen as overly aggressive are much less than you imagine. You can also use this advice when negotiating for an annual raise or even a retirement/severance package.
Chances are that you accepted your current primary job with the initial salary offer. You were happy to get the job and you did not want to tick off your future manager so you accepted what was offered. You most likely are underpaid if that is what you did.