T.,
Frist let me say, I will probably be the in the minority on this one. I am NOT a fan of the ferber method. Frankly, all it teaches your child is that you will not come and help them and they have to fend for themselves. This is not a nurturing environment.
Second, up until the age of about 6 months, babies cry for a reason. It isn't until around 6 months that they start to 'test' mamma and daddy. At this point they will cry in protest of going to bed and try 'different' cries to get you to come more quickly. Then you can start letting them cry for short periods and then going in, reassuring, making sure everything is ok and patting the back or whatever to help them settle down. I have even picked my daughter up (gasp!)to really help her calm down if she is quite worked up. But that hardly ever happens. Seriously... almost never. Typically she will fuss, we go in, rearrange her and then off to sleep she goes.
Before 6 months they cry because something is wrong. They are hungry, they are bored, they are scared, they are wet/soiled, they are hot/cold, they just need mamma (and this is a legitimate reason frankly... they are just BABIES!). Whatever, there is a reason and it is our job to figure out what that reason is.
Third, often times babies will get restless in the night when they go through a growth spurt or are learning something new. It's just the way it is. My daughter now sleeps very well through the night. Waking once around 2am to go to the potty. (yes, she is 8 months old and she goes to the potty. We EC.) However, recently she learned how to sit up from a laying down position. We went through a couple of nights where she hardly slept at all. Consequently mommy didn't sleep either! But, now it is a mastered skill and we are back to normal.
Since your son sleeps on your chest, it sounds like he has a need to be close to you. He is 10 weeks old. There is NOTHING wrong with a 10 week old WANTING to be close to his mamma! It was just 10 weeks ago he was with you CONSTANTLY! 24 hours a day, 7 days a week he was cuddled, held, rocked, fed whenever he needed it (no fussing) and kept safe and secure in a warm, tender environment.
Now, he is on the outside. Bright Lights Big City. New noises, some frightening, new smells, new sights, everything is in extremes for him still. AND he isn't held all the time, he isn't rocked all the time. He is craving your touch mommy... and he's trying to tell you so. He misses you.
Our babies will grow up and be independent soon enough. Why push them to it before they are ready. If you hold your baby 24/7 ... he will not grow up to be a wimpy person who can't take care of himself. Providing a nurturing, loving, and attentive atmosphere will foster the feeling that you WILL help him and you are there for him. It will provide an environment where he can grow to be strong and independent.
I would give him the attention he needs. You may also want to see if there is something causing discomfort. How long after he eats does he not sleep well? Is he hungry? Is he in need of a diaper change? There could be another reason why he wakes up even while sleeping on your chest.