to get married, thus surrendering all power and control to the woman like a trailer being "hitched" to the back of a powerful and all-controlling tow truck
"Hey Uncle Jim, do you know where Uncle Dave is? The game's starting soon..."
"Uncle Dave's hitched, remember? He's smelling candles and buying mattress covers with your Aunt Jane."
'To get hitched for half a monkey' is to do something or to have something done for a bargain (literally taken, it means to get married for just 250 pounds, which is dirt cheap)
What?! Fix your loo for 5 quid? Why do you always want to get hitched for half a monkey?!