Hey ThinBlu,
What kind of Weber do you have?
The BioLite served its purpose well, but you know after a while it's nice to be able to grill standing up! Seriously though, I got it primarily for taking to a tropical vacation spot where the grill situation was always either stolen/broken/rusted beyond repair/no charcoal. Worked great for a long time, but I'm not toting this thing around as much and don't want to sacrifice flavor. I'm blown away by how much knowledge is on here!
A basic on how to do tofu is:
-Start with a block of extra firm tofu (sometimes the extra protein added varieties grill up a bit better, but don't stress about it)
-Open block, drain off the water, then grab yourself 2 cutting boards that are larger than the tofu block. Make a cutting board sandwich in your sink with the tofu in the middle. Add about 10-ish pounds of weight on top and leave it to leach water for roughly an hour. (You want to add enough weight for it to strain, but not break your block).
-Make a marinade (Tofu absorbs flavor well, so don't stress too hard about this; sugars are going to stick a bit more to the grill just like with meat, so maybe go savory for the first cook. I tend to dial it in a bit flavor wise keeping in mind that you're not doing a 6 hour cook, but for now I'd say just use your judgment based on sticking and cook time)
-After the tofu has drained, cut it in half lengthwise, then again. You're looking for 8 rectangles iirc based on your standard block. Generally I'd say keep the pieces larger (little chunks tend to either fall apart into your grill or crisp up too much). For the first cook keep it simple with cassette tape sized pieces.
-Marinate from 30-ish minutes to....? Depends on how long I have and the flavor profile. Let's say 2 hours for the first attempt and call it good! *Reserve your leftover marinade*
-Depending on your grill this is where things get a little up to judgment. I'd typically stick with low and slow for 10 or so minutes. You made need to add a little oil depending on your grates. If you think you're running a little too hot, pop the tofu on foil and then transfer for the final sear and crisping the outer shell.
-Feel free to add a little marinade back on if you want. Or not. Whatever goes!
-Tofu's done when it's squidgy in the middle and crispy on the outside, so no real worry about internal temps =)
Overall I try to cook it as just tofu rather than dressing it up as a meat analogue. It's never going to pass as mock chicken or anything like that, but can be a fun addition to the grill if you want something to top a salad or have some vegetarian/vegan friends. Hope this helped a little bit! There are more complicated versions where you freeze the tofu first or add a cornstarch coating, but generally I just wing it unless I'm really unfamiliar with a particular grill set up. =)