I think this question has been asked many times but I couldn't find it with the search function.

I now have a original 140 x 70 x 15 on my rear wheel but would like a 150 x 90 x 15.
Will that fit or is the rim too narrow.

And then I started thinking....
There is enough room for a wider tire in the swingarm.
Is there also a 160 or 170 rear tire that still fits neatly on the rim or should I look for a wider rim if I want my bike to look realy cool?

What are eye brow bolts?

The stock size tire is a 140/80-15.  That is a very rate size and you are limited to the stock tire manufacturer.  The two best tire sizes to use instead are 130/90-15 or 140/90-15.

A 130/90-15 is almost identical in size to the stock tire.  The actual tire width is withing a few mm and visually you will not see a difference. Actual tread width varies with each different manufacture and tire model, and the stock tire does not have a lot of tread for the 140 size.  If you want crisp handling and good acceleration - this is the size tire to use.

A 140/90-15 is much larger diameter than the stock size and 10mm wider...and it is the largest tire that is "recommended" on the stock width rim.  The larger diameter and heavier weight of the tire slows the acceleration down a bit, and the handling is a bit more sluggish.  The bigger tire also results in a speedometer that is a little more accurate.....as most of the speedometers are optimistic by a few MPH with the stock tire.  This size tire is preferred by riders who do a lot of highway riding as the bike is a bit more stable in a straight line and the gearing is a bit taller.  (Some bikes may rub fender bolts....see below).

A few folks have installed a 150/80-15 tire.  These are heavy and wide - and the heads of the bolts inside the fender can rub on the side of the tire and scrape grooves in the rubber.  The weight of this tire is much heavier than the stock tire - your bike will be slower to accelerate with this big tire.  This width of tire is not recommended for use on the stock 2.75 wide Savage rim - the tire is too wide/short to be squeezed onto that narrow of a rim.

The Savage does not need a wide tire to perform or handle well, and the narrow 2.75" rim makes a 140 tire the widest tire that is acceptable.  When you squeeze a wider tire on the rim you are making the tire carcass narrower and the tread cross section rounder, and that results in a narrow strip of tread in contact with the pavement.  I had a 110/90 tire on my bike for a while and although it looked a bit silly, I never needed any more tire for traction or good handling.......muscle bikes from the 1970's had 4.00-18 tires....which are about 100mm wide!  The wide tires on a Savage are really more of a "Cruiser" appearance requirement....a tire that wide is not needed to handle the available 30HP!

I have a link below for the tire width/height that is recommended for specific rim witths.  USe outside of these recommendations stretches or pinches the tire carcass too much and can affect the tire performance or stability.

http://suzukisavage.com/yabb2.2/Attachments/Tire_Chart.jpg

Eye brows are the chrome bars on each side of rear fender , some support stock sissybar.
Look at the bike from either side , does it not look like an eye brow

Hi all: being a person with more than a few miles under my belt, I've never understood the obsession with wide rear tires.  My standard for tires has always been the Norton Commando, seriously faster than any S40. Standard tires were 3.50/19 to 4.10/19, translating to a max of 120/19.
I currently run 120/90-16,(GS450 rim) totally adequate for the speed this bike can run.
The stock 150 apes the cruiser style, but isn't needed, IN MY OPINION !
Cheers!  
ps: Dave's right, 130/90-15 is ideal for a stock bike
pps: for those that like to play with numbers,
you can see that larger tires reduce acceleration but give higher top speed:

https://www.tacomaworld.com/tirecalc?tires=140-80r15-130-90r15