Interestingly, ligers exhibit behaviour of both species. For example, they can make the noise of both, they like swimming (as do tigers), females enjoy the company of others (typical of lionesses) as well as solitude normally associated with tigers.
The reason they are bigger than the parents is due to breeding strategy and behaviour. In a pride of lions, many males will mate with a lioness, each transmitting a growth-promoting gene so that their offspring will out-grow competitors in the womb; lionesses have a growth-inhibiting gene to compensate. Tigers are solitary animals. A tigress will usually only mate with one tiger. Without this competition for space in the womb, there is no biological need for a growth-promoting or growth-inhibiting genes in the male or female, respectively (and therefore these genes do not exist).
Tigons (tion, tigron, tiglon) are the offspring of a male tiger and a lioness. They are smaller than either parent due to the absense of the growth-promoting gene in the tiger and the existence of a growth-inhibiting gene in the lioness.
Unusually for hybrids, the female ligers are often fertile.