Weak Copyleft licences are free software licences that mandate that source code that descended from software licensed under them, will remain under the same, weak copyleft, licence. However, one can link to weak copyleft code from code under a different licence (including non-open-source code), or otherwise incorporate it in a larger software.
Otherwise, weak copyleft licences allow free distribution, use , selling copies of the code or the binaries (as long as the binaries are accompanied by the (unobfuscated) source code), etc.
Examples of weak copyleft licences include:
The GNU Lesser General Public Licence (or LGPL for short) - this licence was formulated by the Free Software Foundation based on the GNU General Public Licence (or GPL). Its text is longer than the GPL, and it is reportedly a more complicated licence. Other than the general “you-can-link-it-against-everything-as-long-as-you-keep-inclusive-code-LGPLed”, it allows an explicit conversion to the GPL, has patent-related clauses, and contains many additional restrictions.
Version 2 of the LGPL was succeeded by version 2.1, and now there’s also version 3 which is based on a short adaptation of the version 3 of the GPL (see below).
Version 2.0 of the Artistic Licence, which was formulated by the Perl foundation is used by the Parrot Virtual Machine, some Perl 6 implementations, and other projects. The original Artistic Licence has problematic phrasing, and is not recommended for general use, unless possibly when dually licensed with a different licence (as is the case for perl 5 and many Perl modules on the CPAN).
The Artistic Licence version 2 is relatively short and easy to digest. One note about it is that it allows distributing binaries that were derived from a modified source, without the obligation to release the modifications of the source. However, if one wishes to distribute a modified source, he must make his modifications under the same licence.
An anecdote about this licence is that it was chosen by R.E.M for licensing some video-clips from one of their albums.
The Mozilla Public Licence (or MPL) was phrased for the public source release of the Mozilla project. It was characterised as a hybridisation of the modified BSD licence and the GPL. This licence was ruled as GPL-incompatible, which eventually caused the Mozilla project to re-license its code under a triple MPL, GPL and LGPL licence. This is still the licensing terms of Mozilla projects such as the Firefox web-browser up to today.
GPL with an Exemption Clause - the GPL is a strong copy-left licence, but sometimes an additional clause is added that allows it to be linked against code of non-GPL-compatible licences (including non-open-source code). This strategy was chosen by Sun Microsystems when they decided to release the source of the Java programming language under an open-source licence.