6.12.1794 adv Twiss at Inchbald's / 25.5.1795 adv Mrs Twiss at Inchbald's / 27.12.1795 adv Twiss's at Siddons' / 30.1.1796 adv R Twiss at Inchbald's / 3.2.1796 Twiss calls / 7.2.1796 call on Twiss / 8.2.1796 Twiss pp172 / 9.2.1796 tea Mrs Robinson's with Twiss & Tarleton / 20.2.1796 Twiss calls / 26.2.1796 tea Twiss's / 1.3.1796 call on Twiss (not in) / 10.3.1796 sup at Twiss / 13.3.1796 tea Kemble's with Twiss's / 17.3.1796 meet Twiss / 21.3.1796 sup at Twiss's / 1.4.1796 again / 18.4.1796 again / 2.5.1796 call on Twiss (not in) / 5.5.1796 sup at Twiss's / 16.5.1796 again / 24.5.1796 call on Wollstonecraft, with Twiss / 27.5.1796 sup at Twiss's / 28.5.1796 sup at Wolstonecraft's adv Twiss & Wolcot / 1.6.1796 sup at mrs Robinson's with Wollstonecraft & Twiss / 8.6.1796 call on Twiss (not in) / 17.6.1796 sup at Twiss's / 28.6.1796 sup at Wollstonecraft's, adv Twiss / 29.6.1796 sup at Twiss's / 24.7 dine at Holcroft's with Twiss & MALunan / 1.8.1796 sup at Twiss's / 4.8.1796 Twiss & Amelia Alderson call / 17.8.1796 call on Twiss (not in) / 19.8.1796 sup at Twiss's / 23.8.1796 meet Twiss / 25.8.1796 Twiss's at Wollstonecraft's / 7.9.1796 sup at Twiss's / 26.10.1796 again / 29.10.1796 at theatre F Twiss / 10.11.1796 call on Twiss (not in) / 11.11.1796 call on Twiss: dines - / 18.11.1796 call on Inchbald, adv Twiss's, F / 29.12.1796 sup at Twiss's / 15.1.1797 again / 25.1.1797 meet Twiss / 26.1.1797 again / 13.2.1797 call on Twiss (not in) / 15.2.1797 again / 23.2.1797 again / 25.2.1797 meet Twiss / 14.3.1797 call on Twiss (not in) / 4.8.1797 meet Twiss / 18.3.1799 meet R Twiss / 28.5.1799 meet Twiss / 11.4.1800 again / 3.1.1804 adv R Twiss at Philips / 13.6.1807 call on R Twiss / 30.6.1808 meet R Twiss / 5.7.1808 meet Twiss / 31.10.1808 meet Twiss / 7.11.1808 Twiss calls / 5.3.1821 R Twiss dies
The GD website has coded all plain Twiss entries to Francis Twiss and only R Twiss entries to Richard. That it should be (mostly) the other way round becomes clear when you look at the letter dated 6.2.1796 (Abinger c3 f18r) from Richard Twiss to Godwin, proposing that Godwin should dine with him on Tuesday and then take tea at Mrs Robinson's. Godwin in fact called on him the next day, and though he didn't dine with Twiss on Tuesday, he took tea with him at Mrs Robinson's, which was Godwin's introduction to her. And he read Richard Twiss's book (about France in 1792) the night before. Godwin had first met both the Twiss brothers, and Mrs F Twiss, at Mrs Inchbald's - the Twiss's at Siddons' were presumably Mr & Mrs F Twiss as Mrs T was Mrs Siddons' sister, but Twiss's might also mean the two brothers. Richard was unmarried. Since Godwin doesn't use an initial for Twiss between 30.1.1796 and 29.10.1796, and then it is F, and F again on 18.11.1796, I think it's clear that all the plain Twiss entries after 30.1.1796 refer to Richard, except for 13.3.1796 tea at Kemble's with Twiss's, and 25.8.1796 Twiss's at Wolstonecraft's. The Kembles were the family of Mrs F Twiss and Mrs Siddons. The form Twiss's was Godwin's usual way of noting a couple or members of one family, except when after 'at' when it usually meant at someone's house. After Godwin married Mary Wollstonecraft, he only met Twiss once in August and then again two years later, when he used R Twiss again, then the next 3 meetings he just used Twiss. After a gap of 4 years he used R Twiss for the next 3 meetings, then plain Twiss again 3 times. Godwin recorded his death as R Twiss but didn't record the death of his brother in 1827,and F Twiss (transcribed in GD website as T Twiss) was inserted and then crossed out towards the end of 1794 in Godwin's 1796 list, while R Twiss, near the start of 1796, was not crossed out.
This adds up to a good reason to suppose Godwin had quite a close bachelor friendship with Richard Twiss which ran simultaneously with his courtship of Mary Wollstonecraft. Twiss may have encouraged Godwin into probably his first sexual relationship, either directly or by competition.