You can look up postage rates to the US on the Royal Mail website. It will usually go on package weight, but there are also various delivery options. Regular airmail usually takes about 1-2 weeks and starts at 60p (usually that price will be for a regular letter), but you also have faster delivery choices or you can even send surface mail, which is cheaper, but takes about 6-8 weeks to arrive in the US (this time of year though, it's likely to take longer due to Christmas).
My flatmate has left a Sunday Times on our kitchen table, so I've just weighed it - it's just under 1.5 kg with the magazines and everything. According to the Royal Mail website a package of 1.5kg to the USA will cost anywhere from £10.31 (56-day surface mail) to £28.59 (Airsure, from 4 days delivery) and if you use Parcelforce to send it, it's going to be between £30 and £55!
I'm guessing it would cost you about £5-8 to send it by airmail, but I could be completely wrong.
According to the quick search I just did, regular Airmail for a 1.5kg package is more like £18!
