I would not worry about weight, nor size; around that time (over 200 years ago) the measurements were not exact like nowadays - mine below is more like 28mm, for example.
The 1/4d was 23mm (4.9g) and the 1/2d was 27mm (6.3g) and the 1d was 34mm (18.9g).
So yes 8.8g is more than 6.3g but is certainly nowhere near 18.9g, and similarly 29mm is nearer 27mm than it is 34mm. So it is a UK HalfPenny 1771 date.