How relevant is current salary during negotiations compared to market avg?

Say you make $80k (total compensation) but you are way underpaid (simply because it’s a small company in a smaller city) compared to market average of say $150k (total compensation) in a bigger city (e.g NYC).

Given that you are looking for a job in the bigger city, is it ridiculous to ask for the average market pay given that this would be almost double your current salary?

NY cost of living is likely 2x as high as in a “smaller city”, so no. Anyway, if you’re talking about the $100k sort of range all in, it means very little to most employers, unless it’s a small company with a tight budget. If you’re looking for a job at a large firm, the division normally gets a budget for, as an example, an associate, which is defined as someone with X years of experience and is paid between say $100k and $200k. There isn’t really much incentive to not offer you the same as any other applicant, because it’s not like the manager pockets the savings.

Thank you sir, your input is always appreciated

If it’s a small company they may try to nickel and dime you even though that strategy will mean they end up with not the best hires. That’s on them. If it’s a big company they will (as ohai pointed out) already have a range budgeted out for the position that is aligned with CoL in the city. You really should not have to negotiate for market comp. If they tried to negotiate based on your prior salary then I would be very cautious.