Let's start with, "Which chart to I follow?" This is the source I use for weight/volume conversions: FareShare Recipe Exchange: Volume to Weight Conversion
It's got a lot of different ingredients of enough types that you can extrapolate anything they don't have.
Now let's talk about accurate measuring: I can't overemphasize how overemphasized accurate measuring is. People get the idea that baking is a sort of molecular chemistry where measurements to the nearest nanogram are important. That following a recipe exactly is a guarantee of success, and deviation a sure path to failure. Thank goodness those things are wrong.
Recipes in normal household sizes are very rounded off, and are almost always forgiving of minor deviations. For instance, if you use 4 medium eggs instead of 3 XLarge, or if you use 1 tbs of baking powder to a scant cup of flour instead of a slightly rounded cup -- those sorts of things don't matter at all.
Why? Well, for one thing food chemistry isnt' all that sensitive. For another, the recipes themselves are written in convenient amounts more than exact ones. That's because even measured quantities vary with environmental conditions. For instance 110gm of AP flour on a day with 30% humidity is not the same as 110gm of AP flour on a day with 80% humidity. The variance is not weight but the ratio of flour to water -- what bakers call the percentage of hydration. It's an important thing -- but not enough to change your recipe much.
Get your measuring cup, some flour, and tare off a bowl. Start measuring four cups of flour into the bowl, one at a time and note each measurement. Was the weight of each cup exactly the same? No. Was the total range of deviation within 10gms (about 1/3 oz)? Probably not. Do you think a couple ounces of flour out of a pound is going to make a difference in a cake? Doesn't matter what you think, it won't.
What was the actual measurement they're converting? Did the first baker tamp her cup of flour down, wipe it with a knife, do anything else to make it "accurate?" Important questions if exactness is important, because all those things that make volume consistent for any given baker, make volume inconsistent from one baker to the next -- because each is doing something different.
Measuring by weight is sometimes more convenient. But because of environmental factors, especially humidity, It gives more of an illusion of an reproducible accuracy than reproducible accuracy itself. To some extent, its popularity in home kitchens comes from its near universality in professional bakeries. However, the situation in a professional bakery is very different. In a bakery you use flour by the (weighed) bag weight -- not by the scoop (at least not at first). Doughs are made in amounts to large to handle by hand -- so the baker has no opportunity to use her sense of feel. Bowls are too deep to look into, so even sight conveys limited information.
You already know this (if you think about it). You check cakes for doneness with a toothpick and breads with a thump -- not with a clock. Even when you know your oven. It's the nature of food. Look at it this way. Food costs money, and attention is the least expensive ingredient to pay.
Here are some common sense rules (Fair warning, most important comes last):
Close counts in horseshoes, hand-grenades, and baking
If it tastes good, you can be off by more.
If there's a big variance between one conversion and another, or one recipe and another -- be like Buddha (WWBD?) and take the middle path. So 120gm, 110gm? Use 115, you'll be fine.
If it's a little amount in a big recipe -- measure that one carefully.
Watch out for recipes that call for things you KNOW are wrong: For instance if a recipe calls for more than 1-1/4 tbs baking soda per cup (115gm) of flour; or 2 tbs of oil instead of 3/4 cup of shortening to make biscuits. Doesn't mean it isn't right or won't work -- just make sure your glasses are clean and you read it correctly.
If it's a big amount you can be off by a little, no problem. How much is a little? 10% or less is a little. How much is time to worry? 20% is too much deviation. What about in between? WWBD?
If you feel like you're measurements are off, do what you can to adjust on the fly. Which leads to the biggie:
Use your senses to keep track of your recipe. Does it feel right? Does it look right? Does it smell right? Feel is the most important thing in baking, and seldom discussed.
Case in point: My daughter, a good cook and still improving, came to visit us. She and her boyfriend made dinner, and for dessert, made a cake. Our stand mixer was being repaired, she didn't want to use an electric hand beater so decided to use a whisk. I heard her whisking from the other room -- I know the sound of good whisking -- and hers sounded good. But, then came the kvetching (complaining). The eggs weren't cooperating. She brought in some thin, pathetic eggs and the whisk -- so I could "fix it Daddy." Aha! The whisk she brought was the wrong one -- a heavy wire type -- no wonder she was having trouble. I switched to a thin wire whisk with more balloon and she watched the eggs take in air, change color to lemony, and thicken to almost a saboyan -- like magic (Daddy's still got the wrist -- even if no props from his daughter). Then we whisked in the dry ingredients with the heavy wire whisk. The wets and dries came together quickly, the batter soon running off the whisk in a wide, satiny ribbon. We went and bought both types of whisks for her the next day.
So, where's the measuring? Exactly! Where's the measuring? Which do you think was more important to the cake? The texture achieved by technique? Or, whether there was 2 tbs of extra flour in the batter? Lightbulb should be on.
Moral of the story: Don't sweat the conversion charts, they're not that important.
Hope this helps,