I hope you know someone that you can sell the tire to when you find out it's too wide to fit.

Installing a (deflated) Metz 160 is a real tight fit with literally no room to spare, and it's 6.37" wide. The Avon Venom 160 is 6.6" wide.

The Avon 160 is also 1.0" taller than the Avon 150, so you'll need 1/2" more fender clearance.

Good Luck

 

Interesting.
I'm currently running Avon Azaro 150/80ZR16 and it seems I have half an inch space between the tire and drive belt. What room should I be worried about if going for wider tire?

 

Also a 160 is just too wide a tyre for a 3" rim. Not wise IMHO! I'm working to fit a 4.5" rim into my Glide, so I can use a 160 Avon.

 

As I've said repeatedly, tire sizes and inflation pressures vary by both brand and models within the same brand.
Metezler RECOMMENDS their ME880 160/80-16 as a replacement for the stock 150/80-16 on a 2004up Sporty, and the Metezler Tire Fitment Guide spec's the appropriate rim size as 3.00"-4.50".

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