why don’t men have to mourn their dead wife while a woman has to mourn her dead husband

this is something that has been bothering me for a while and I was hoping someone could answer or educate me on this topic. when a woman's husband dies she must wait 4 months and a couple of days before getting married. I understand that this rule is put out in case the woman is pregnant. However, the woman is not allowed to wear jewelry, perfume or anything that may beautify her in order to show respect to her husband who has passed away. she cannot go out with friends to feel better and can only leave the house for necessity. I don't think this is necessarily bad but what bothers me is that when a mans wife dies, he does not have to show any respect or mourn his wife's passing away. in fact he can marry someone else a day after her passing away. isn't there some kind of respect shown for a wife who's passed? why is a wife worth so much less than a husband? it's starting to seem like a wife is required to love and respect her husband more than he is required to love and respect her.