If you are looking to get cut, yes of course you will see the results of your efforts more if there is not too much body fat covering your hard-earned muscles.
But, you need to HAVE muscles!
If you overdo the cardio, you are in danger of burning lean tissue as well as fat. Don't forget that resistance training also burns energy.
I have always tended to try to incorporate as much cardio as possible for the same reasons as you, but my trainer told me to reduce it to 2-3 sessions a week, and to do good, solid work with weights for 3-4. But you need to work hard. There is no point in sitting at the chest press doing 3x8 at a resistance you can already cope with. You want cut? Then you must work muscle groups to failure.
If I were you, I would do three good weights sessions a week, (upper body + abs, lower body + abs and upper + for week 1, then week 2 is lower +, upper +, lower +) If you must do resistance and cardio in the one session, do your weights first, doing lighter weight warm-up set then working to the max. Use your cardio for your cool down - and that implies not overdoing it.
Don't overlook nutrition. On weights days, eat some good carbs an hour before work-out, and be sure to get some protein into you afterwards. (All that has a calorie cost, so keep that in mind.) On cardio days, work first thing in the morning on an empty stomach. Re-fuel afterwards, and whatever you are doing, keep well hydrated.
Get some expert advice from your trainer - a trusted member of your gym staff or somebody who works and gets results. There is so much sound advice available on the internet - and some rubbish that is essentially advertising for dubious products.
Hope this helps.
Regards,
Alison