Soldering iron tip grinding

DON'T grind your soldering tips. It will ruin them. Good quality tips are made from copper with a thin layer of iron or another metal on top. The copper conducts the heat, and the other metal prevents the copper from corroding. You can buy new tips of any size and shape you want. They are pretty cheap. There is usually a tiny screw on the side of the soldering iron near the hot end that lets you change the tip.

Here's a cross-section of what's inside good tips (image by Hakko)

Do not grind your tip. Tips are usually made of copper with iron plating. The copper transfers the heat well but would get eroded away too quickly by the solder. So what to do?

First, a plain conical tip isn't such a bad thing. That's what I mostly use for all kinds of soldering. Dead bug soldering usually requires less heating power, since there isn't a copper trace acting like a heat sink attached to the pin. A plain conical tip should work fine. Try it.

Second, many soldering irons have interchangeable tips. You only said you have a Weller, but not what model. Weller makes a lot of different soldering irons. Some good ones which definitely have interchangeable tips, like the popular WES51. They also make low end soldering stations aimed at people that don't know much about solder and buy on price. Some of those may not have interchangeable tips. The kind of people that buy a $40 soldering station because it costs less than the $45 soldering station don't think about changing tips when they buy, so the soldering station is designed for lowest possible initial price, even if maintainance costs more in the long run.

You get what you pay for.

I agree with the other answers that you shouldn't grind a tip that is still in good condition.

However, if you ever happen to have poor quality tips or tips that have weared out, you can use a file to reshape them. The downside is that as the copper corrodes, you'll usually have to repeat this every 5-10 times you use it. Eventually the tip will have been filed so short that it is no longer usable.

I do this to get big flat tips, which I only need rarely to solder bigger components.