What is the difference between lightweight tweakable block cipher and tweakable block cipher? For example, lightweight tweakable block cipher is SKINNY family, and tweakable block cipher is Threefish cipher.
In the case of SKINNY the first column in the comparison tables lists the area as GE value. GE is the "gate equivalent", I'll quote Wikopedia on this one:
A gate equivalent (GE) stands for a unit of measure which allows to specify manufacturing-technology-independent complexity of digital electronic circuits. For today's CMOS technologies, the silicon area of a two-input drive-strength-one NAND gate usually constitutes the technology-dependent unit area commonly referred to as gate equivalent. A specification in gate equivalents for a certain circuit reflects a complexity measure, from which a corresponding silicon area can be deduced for a dedicated manufacturing technology.
So it is clear that the lightweight part mainly means that there are few requirements with regard to the amount of gates on a hardware chip implementation. The amount of gates indicates the complexity and size (the area) of silicon required on a chip. The larger the chip the more complex the design and - of course - the more expensive the chip. The performance and security should still be within acceptable bounds though.