Mosfet controlled LED strip not bright enough
Fortunately, the graph you want is actually next to the one you used and I have marked red lines on to explain where you problem is: -



So, on the graph on the right (the one you used) I have marked a vertical red line corresponding with a gate source voltage of 3 volts. Now, at the point where the red line hits the traces if you looked across at figure 1 you can see what that means. Note - the current is about 13 amps.

Can you see that the 2nd line I drew (the horizontal red line) crosses a bunch of traces in figure 1? It doesn't cross the lower trace (not quite) and that is the trace when \$V_{GS}\$ is 3 volts - this means that driving it at 3 volts isn't going to deliver the goods (13 amps) typically.

Take the next trace up where \$V_{GS}\$ is 3.5 volts - you can see that my horizontal red line crosses it at a drain source voltage of about 0.7 volts (vertical blue line). This typically means that if you wanted to deliver 13 amps to your load, the MOSFET would drop about 0.7 volts from drain to source.

If you drove \$V_{GS}\$ at (say) 10 volts, can you see that to deliver 13 amps, the MOSFET would drop about 0.35 volts (vertical green line).

Given that you only need 0.5 amps I would say this MOSFET would drop significantly less than 0.1 volts across drain and source even when fed with a \$V_{GS}\$ voltage of only 3 volts.

So, my conclusion is that it can't be the MOSFET that's giving you the problem. Maybe it's the interconnecting wires or your power supply isn't able to deliver the current you need. Maybe your MOSFET is "fake"?


  However it is my first time looking at a datasheet so that's probably
  where my mistake is, though I have no clue what


Hopefully this clears up where the problem doesn't appear to be - use fig 1 in future - it delivers what you need to know in this respect.