What are the speaker specs? And what volume did you turn it to/what is the max?
Is this same issue happening if you were to try it now, or when the volume is cranked, does it immediately crackle (or sound like feedback?) Also, what input are you using? Iphone 4 and 4s are notorious for producing feedback at high volume. The charge of the phone and the charge of the system isnt equal, so this causes a very audible crackle at higher volumes. This doesnt sound like your issue, but its something to think about.
Personally, I suggest rewiring for a speaker amp. A nice 4 channel, 500 or 600 watt amp would be perfect in this scenario. You could run the small speakers from the head unit and the 6in from the amp, or all from the amp. From a stock head unit with aftermarket speakers, sound quality at high volumes will always suffer, and like people on here have suggested, the impedance won't always match between the two. An amp gives you much more flexibility. If your 6in speakers are rated for 200 watts max, they can probably handle 60 watts of continuous power (Im using Polk Audio 6in speakers as an example). Your head unit puts out a MAX of 50watts (mine maxes at 42 LOL) so thats only 10-15 watts continuous power. This means you are essentially running your speakers at 1/4 the potential. Stock speakers sound great from a head unit because they were designed to run at that wattage. Aftermarket speakers, on the other hand, produce excellent quality and clarity, but in order to do that, it requires more power. Your head unit will make those speakers sound great at low volumes, but as soon as you crank it up, it sounds like crap because the speakers are being severely under powered.
Just something to think about... A good speaker amp costs only 100-150 bucks and it will tremendously improve sound quality. It will need only about an 8 or 10 gauge wire from the batter as well, so it will be easy to wire, configure, and hide. Currently I have a 12 inch sub with a dedicated amp (im not some gangster listening to hippidy hop, i prefer good ole country LOL) and a four channel speaker amp under the backseat of my YJ. I can crank the volume wayyy up and it sounds great. At 70MPH with the top and doors off, I can still clearly hear my music (cops probably can too! LOL). I do a lot of commuting, so this was a decision I made so that I can commute in my jeep and not get bored
Im not necessarily saying that this is your problem. Im just saying its something to consider