I've seen a lot of this misconception around the internet. The thickness of the stylus has nothing to do with it. It is a limitation of the touchscreen technology itself. Manufacturers make the styluses thick for two reasons: 1. to avoid damaging the glass, and 2. to avoid lying to you about their effectiveness.
There is even a company that makes styluses with pinpoint accuracy:
But I have seen a demo of these things, and if you attempt to write at a natural speed, it looks just as horrible as anything else. Stylus makers are making a killing off of people like you who think that if only they get a better stylus, they'll be able to write on their tablet...
Like I said, the real problem is the screen technology. Most tablets out there use capacitive touchscreens, which are good because they have a low profile, low power consumption, can respond to your fingers, and can easily be used for multi-touch. The problem is that capacitive screens are not very accurate (only to within about 5 pixels), so they are not useful for the fine, quick movements used in natural handwriting. There is another kind of screen called resistive, which is not as convenient as capacitive because it requires a sharper object like your fingernail or a piece of plastic (think signature windows at store checkouts, or the old Palm Pilots, etc.), although resistive screens ARE a little more accurate.
What you really want, if you want to write naturally on a tablet, is a screen with an active digitizer
. This is the technology Wacom uses for its drawing tablets. It requires a specific pen for input, and will not allow multitouch input at all (unless you get a "hybrid" touchscreen with both capacitive input and an active digitizer pen). It will add more bulk (making your device slightly thicker), and it consumes a lot of power (think 4 hrs battery life instead of 7), but if you want to write and draw, it's the only way to go. It also costs a lot more (think $800 instead of $500).
Active digitizer screen technology has been on tablet PCs and slates for over 10 years (curiously, Apple never bothered to produce a tablet PC with active digitizer, despite being thought of as the go-to computer company for creative works). The forerunners have been Fujitsu and Toshiba; now you will also find machines by HP, Lenovo, Asus, and everyone else.
I use a Fujitsu T5010, which is a convertible laptop/tablet. It will not really suit your needs, because it is a full laptop and will be too heavy to do what you want. But I write and draw on the screen all the time; in fact, I've done all my homework and research on this thing for the last 4 years, practically eliminating wasted paper. My screen literally IS a Wacom tablet (the laptop case sports a Wacom branding sticker next to the usual ones from Windows and Intel).
However, you will find numerous slates (that is, tablet PCs that have no keyboard or optical drive), although they tend to be expensive. Some of the cellphone makers are also catching on to the need for an active digitizer on their 10.1'' tablets, so look around.