Why to some large companies use tm instead of ®? For example, Skype uses ™ instead of ®.
This is the point of my website: how small companies use intellectual property differs from large companies. Skype (a large company) has to comply with the laws of many nations, small business generally operate in a single country and need only comply with that single country's laws. More importantly, this website is about United States laws.
Large companies may be directing their advertising to purchasers in several nations. Large companies frequently have a presence (offices, equipment, employees) in several nations. Your example, Skype, is clearly one of those companies. So, Skype must comply with the trademark laws of all of those nations. Those laws are likely different; the status of their trademark registrations in each of those nations may be different. As a result, the use of the ™ symbol may be more convenient and consistent for them.
Small companies generally sell (most) of their goods in their home country. They usually have a single (or maybe a couple related) trademarks. They are usually only worried about their home country's law (they are rarely present in foreign countries, except on vacation/holiday). So, they they can more readily use the ® symbol.
Of course, I am a US attorney, and, I write about US law. If you are in London, England (rather than London, Ohio, or London, Kentucky), then your rules (while similar) are different. It is worthwhile to have a solicitor (the UK word for "lawyer") review your trademarks and how you are doing your marking.