What effect does resistance have on a diode's characteristics? (regarding IV curves)
Detailed diode theory is well-documented in any microelectronics textbook. But the simplest diode equation that results from such detailed analysis is the Shockley diode equation:

$$I_D=I_{S\left(T\right)}\cdot\left[e^\frac{V_D}{n\cdot V_T}-1\right]$$

\$V_T=\frac{k\cdot T}{q}\$ is based upon statistical thermodynamics and is called the thermal voltage. \$T\$ is the absolute temperature, \$k\$ is Boltzmann's constant, and \$q\$ is the charge on an electron. It is typically about \$26\:\textrm{mV}\$ at room temperatures. \$n\$ is a model parameter called the emission co-efficient and will usually be around 1.7 to 3 for diodes, but may be as little as 1 and can be (infrequently) higher than 3. \$I_{S\left(T\right)}\$ is the y-axis intercept (log chart) of the diode behavior and is also significantly quite temperature-dependent (on the order of \$\propto T^3\$ to \$\propto T^4\$.)

You will note that this equation does NOT include any external, added circuitry elements. It provides a simple relationship between \$I_D\$ and \$V_D\$. In your comment, where you say you are only trying to observe these two parameters, you will expect this behavior without regard to an external resistor.

It's that simple.

(Well, not really. Diode behavior is a little more complex than one equation provides. There are limitations in reverse voltage, current crowding issues, various and multiple surface and volume re-combination issues, physical bonding wire and structure related issues (Ohmic resistance, for example), etc. All of which make even a simple diode more interesting at times.)



Don't be confused into thinking without nuance about this, by the way.
Similar equations model the BJT and are similarly independent of the external circuit elements surrounding a BJT. But not all concepts important to the use of a BJT are independent of the surrounding circuit elements. For example, BJT switch-saturation IS a function of external circuit elements and not purely a function of the BJT itself. If you look at BJT models, you will not see any discussion of switch-saturation. That's because it's not a function of the BJT itself, but of the BJT as part of a circuit.

In short, you always have to engage your brain. You never get to just take a free ride or ignorantly apply pre-conceived "bright lines." You must apply element and/or circuit behavior, appropriately. To do that you have to think with good mental models appropriate to each circumstance.