Depends on whether or not the "non-gambler" has any heart or not.
I don't gamble much myself but if I was to play someone that played at my same skill level I don't think I would expect to get any weight just because I don't gamble much. Instead, I would tell myself I can beat this guy - I would then step up to the table and give it my best shot.
There's definitely something to be said for playing outside of your gambling comfort zone. I guess if a player that was my equal wanted to play for an amount of money that I wasn't comfortable playing for then I would just decline the game. I can't see asking for a spot in those situations just because you aren't as experienced of a gambler. I guess it doesn't hurt to try but that's just not my style.
If you really think about it - it's a horrible frame of mind to enter into a matchup with. What you are ultimately telling yourself is - "yes I am as skilled of a player as him, but once something is on the line I'm going to really suck!" Okay, so now you get a small spot. How does that change your mindset? It really doesn't. Your mindset will still be negative. Now you tell yourself - "well, I'm still going to suck really bad because we are betting something, but maybe I will get lucky and he will give me the match." That's about your only chance in that situation.
This is really the only time I agree with the idea that you really just have to step up and take your lumps. I don't agree with the idea that you need to constantly gamble with better players (giving them your money) to get better. But when it comes to playing players near your speed you just need to go for it.
Now, if you are just a nit lock artist that just gambles when you have the best of it then this post is not for you. Instead, just keep hanging around the pool hall until you can make your 40 dollar score. The rest of us guys are busy trying to get better.