At 51 grams, it's definitely not a penny. But at only 51 grams, it's quite a bit lighter than a twopence (these "cartwheels" weighed exactly 1 avoirdupois ounce per penny, so a twopence is supposed to weigh 56.7 grams).
Yours is badly worn and/or corroded, so I'm thinking losing 5 grams might be reasonable. I'm fairly sure it's not fake; making a cast fake twopence seems like a lot of trouble to go to for a coin that never circulated much so would likely have been closely examined if received in change.
You might even have a "dishonest weight". Merchants used to use cartwheels as shop weights and people trusted them because everyone knew exactly what they weighed. But a dishonest merchant might have tried to deliberately lighten up your coin - a nice long soak in vinegar might have done the trick - to make his 2 ounces slightly lighter. I own a very worn cartwheel penny that had some of the metal shaved off the rim on one side, presumably for a similar reason; if you put it down on a balance pan you wouldn't notice it was missing several grams of metal.
Don't say "infinitely" when you mean "very"; otherwise, you'll have no word left when you want to talk about something really infinite. - C. S. Lewis