I've heard that its better to weight train before the season starts so it gives you a good base, but then how much should you continue to weight train during your competition season? And how much do you think it could improve my time? I run a 1:43 half marathon, but my training isn't that structured.

you can do weight training. But focus on high reps with low weight, otherwise you will bulk up with too much "fast twitch" muscle fibres, which will just slow you down over long distances.