My first reaction is, how much is he getting during the day?? My girls only had 2 or 3oz bottles at that age, or they were breast fed, and very 2 to 2.5 hours. Night time was every 3 hours, and by 3 months it was every 4 or 5 hours.
In my opinion, you should consult your physician. The most recent researh that I've heard about suggest that solid foods of any kind introduced early are associated with allergies later in life. And there have been incidents of choking with small babies and cereal in bottles.
The APA recommends 4-6 months, and ideally 6 months if the baby is breastfed.
I'm assuming you're feeding formula in the bottle and not breast milk? If it is breastmilk, the problem could be hind milk v. fore milk consistency. But if it's formula, make sure you're mixing it correctly (I know it's a silly thing but it happens). But also, the little guy is just 7 weeks old! He's hungry! He doesn't know what time of day it is. Before you start putting cereal in his bottle, I would recommend the following...
Try to slowly increase the size of his bottles very slowly (1/2 oz. to 1 oz.) during the day, and feed him more frequently during the day (every two hours). Overall, your baby will still be getting the same number of ounces, but you might find that he is comfortable stretching out his feedings at night more. Also, he might be waking in the night for something other than food. Are you sure he's hungry? Do you swaddle him? Some babies get very startled at night by their own movements and swaddles help alot. Try rocking, singing, shushing, swaying, and a tight swaddle, and see if that helps. Also, keep the room quiet and dark, and keep eye contact to a minimum, so that he stays sleepy.
Lastly, many many babies eat every 2 to 2.5 hours for months. It's really not that unusual or extreme. It just sucks for moms after many many nights. See if a friend, partner, grandparent, who might be willing to take a night shift so you can rest. Once you get some rest you might be able to deal for a few more weeks until he slows down at night.