Proton NMR Spectrum for Nicotinic Acid
First, a great source of information on this kind of problem is the website of Hans Reich at UW Madison, see e.g. here. Couplings can occur with protons at ring positions ortho, meta and para, with typical values of $\pu{7-9}$, $\pu{2-3}$ and $\pu{&lt;1 Hz}$, respectively.  

This  is (roughly) the information I extracted from your spectrum:


$\pu{  9.15 ppm, \space d,  \space 1.5 Hz}$ 
$\pu{  8.83 ppm,\space dd, \space 5 Hz, 1.5 Hz}$
$\pu{  8.3 ppm, \space dt (apparent), \space 2 Hz (t), 8 Hz }$
$\pu{  7.6 ppm, \space m (ddd),   \space 5 Hz, 8 Hz, &lt; 1 Hz}$


You should report the field at which the spectrum was acquired since otherwise the magnitude of the J couplings is ambiguous. Assuming that the largest J is $\pu{8 Hz}$ leads to the guess that it is a 400 MHz ($\ce{^1H}$) magnet. You should also report the solvent.  

Second, your spectrum is very nice, showing great resolution. Compare for instance to this spectrum (also at 400 MHz but presumably much higher concentration -  $\pu{100 mM}$). Either the concentration of the solvent and temperature may be reasons you obtain higher resolution, resolve very small couplings. The BMRB spectrum was acquired in D2O, pH 7.4, 298 K. Your spectrum was acquired perhaps in $\ce{H2O}$, and perhaps at low pH, resulting in protonation of the pyridine N, but probably not.



Based on the structure you expect 2 to have the weakest couplings to other H. It displays a small coupling, not easily quantifiable because you clipped the spectrum in the figure. 5 Is expected to be a doublet of doublets, with both couplings similar and large. It also displays a smaller third coupling. Therefore lets start by tentatively assigning 2 to the resonance at 9.15 ppm, and 5 to 7.6 ppm. The resonance at 8.3 ppm is an apparent doublet of triplets, the triplet splitting being small, 2 Hz, the larger 8 Hz matching up with that from 5, so this H is vicinal to 5. One of the smaller couplings is presumably to 2, the other to 6, explaining the apparent triplet multiplicity. The last resonance, at 8.8 ppm, has a coupling matching up to 5, and another smaller one to 4, so we assign this to 6. So, to summarize, here are the assignments:


$\pu{  9.15 ppm, \space d,  \space 1.5 Hz, \space }$  2
$\pu{  8.83 ppm,\space dd, \space 5 Hz, 1.5 Hz, \space }$ 6
$\pu{  8.3 ppm, \space dt (apparent), \space 2 Hz (t), 8 Hz , \space }$ 4
$\pu{  7.6 ppm, \space m (ddd),   \space 5 Hz, 8 Hz, &lt; 1 Hz, \space}$ 5


This matches your assignments and those in the BMRB. So this analysis explains the small coupling for 2. The simplest explanation: that's a meta coupling to 4. It does not explain the small coupling for 5, though. That might be a trans coupling to 2. 

The magnetization transfer pathways between the assigned H can be verified by inspecting the $\ce{^1H-^1H}$ TOCSY available at the BMRB. In particular, there is no pathway between signals at 9.1 and 8.8 ppm.