I am having an issue with my 2000 Savage where it feels like there is some kind of either hesitation in the motor or drag on the bike. I get this when throttle is steady and occurs through various speeds and happens every second or so. Any ideas on what I should check?

Location is right at sea level, I am unsure about the carb and it looks like the cover is still over the mixture screw so no adjustments there. Exhaust is a supertrapp put on from a previous owner, air filter is stock.

I have not had the bike for long, but it was not doing this a few weeks ago, it just started happening recently for some reason.

Has this problem been present since you got the bike or is it a new issue?  Does it happen all of the time or only when it's hot or cold outside? Does using partial choke make a difference?

Batman is probably right, but if you have a stock petcock, I would replace it or run it on PRI.  The stock petcocks cause issues sometimes.

Next, I would check the condition of the slide, make sure it's clean, and make sure the diaphragm is seated properly.   Mine was worn and it caused a few different issues over time.  When it sticks, it feels like the throttle just doesn't work.

Once you have eliminated potential issues you can look into jetting adjustments as batman suggested.  But, you never want to attempt to jet around a potential mechanical issues.  You'll just be chasing your tail.

You mention it wasn't doing it a few weeks ago. If it is as Batman suggested, the carb tuning, then it is possible that changes in weather/season can affect the running - similar to elevation.

Where I live we can have extremes between high humidity or very crisp mornings, depending on the season.

We're just coming into Winter here in Australia and my bike has started to feel a little 'leaner' than it did a few weeks ago. When I tuned the carb (in Spring), I turned it just rich enough to eliminate the surge and the backfire. It ran like that all through Summer and Autumn. Now that the mornings are getting cooler I get a slight backfire occasionally on gear changes (thankfully the surge hasn't returned ... yet!)