Increasing the size of your tires in LFS tweak... does it actually make any differnce to the overal grip levels???

They can get to wide though. Then they dont help at all anymore.

Try making a 155/60r15 and drive around with alot of horsepower (Not sillymuch, but 3-400). Try doing a hard launch.
Then try making those into 250/30R17's instead. Try doing a hard launch again.

they affect the handling in meaning of weight, the bigger they get the heavier they are...
obviously.
and you can use big ballonish tyres for fun purposes (curbs aren't that dangerous anymore) but you won't be able to break some times.
I love to roam a bouncy env. with big ballon tyres (saw these things in a documentary about awd trucks roaming the ice deserts of our planet)
keep experimenting...

regards

Of course tyres have an effect on handling.