I would also recommend sizing your fork springs to your weight as the first step to upgrading your suspension. But I definitely would NOT bump up the oil level from stock, and would NOT go with heavier fork fluid.
The main problem with most production forks is that the oil level is too high to begin with. It allows the manufacturers to put in (relatively) soft fork springs, which most street riders find more comfy, while still maintaining some bottoming resistance. The problem with this approach is that the highly progressive nature of the air spring makes the bottom 1/4 of travel waaaay too harsh, while the lightly-sprung initial 3/4 of travel allows you to dive right down to it. So... you dive, then hit a 'wall'. The forks may not mechanically bottom w/ a high oil level, but the feel of them will be very close to the same. The result in either case is suspension that doesn't move. And when suspension doesn't move, it's not working.
I've yet to work a set of forks that, once properly sprung, didn't require the oil level to drop significantly from stock recommendations. We typically set anywhere from 120mm-140mm, depending on other variables.
As far as oil weight goes... going w/a heavier oil may make the bike 'feel' like it handles better, but only because you've bumped up the compression damping, giving the bike a more solid platform. Turn transitions feel great... until you hit a bump or need responsive traction when loaded up in a corner. Then the suspension can't react fast enough, causing you to lose traction, and in the weeds you go. Proper valving coupled w/ proper springs, proper oil weight, and proper oil level can provide both a solid platform during transition as well as the ability to soak up pavement irregularities. But just bumping up the oil weight w/o doing anything else will generally make the compression damping too harsh.
FYI - there are benefits to going with lighter fluid weights, assuming you valve accordingly. The most common weight most suspension tuners use is 5wt (which, as surreal accurately pointed out, can vary according to brand).
If you're up to getting your forks revalved & resprung, rock on! Oil weight & level will be dictated by who does the work and what method they use to achieve their goals. But I'd leave the oil weight stock if you don't revalve. And if I did anything with the oil level, it would be bring it down, & get springs to match your weight & riding style.