The keys to making a a good deal is circumstance, timing and need.
You’ll always struggle to make an arrangement after the fact.
Now, if tightarse had come to you to ask for a lift, “tomorrow” which had evolved over time into a full time arrangement, then you could quite easily ask for some petrol money, but you offered so you screwed up the circumstance and it’s past the first few awkward days, so you screwed up the timing – you’re now ‘friends’ the only thing you have left is need.
Tightarse needs to get to work and home again, he has some options, walk / ride / bus / lift. I assume because of the distance walk is out or we wouldn’t be here now, I guess they’re not a cyclist either, or it’s not practical – leaves the last two – one is free, a lift to work with your ‘friend’ chat shit about the TV last night, moan about the Mrs etc, the other is one of life’s little miseries, no one likes the Bus apart from Nanas because they get to go in the middle of the day when there’s only other Nanas on board and they don’t have to pay, for the rest of us it’s a bit shit.
Personally I’d say “Morning, sorry this is a bit awkward, but you know I’m happy to give you a lift, but do you mind if a formalise it a bit? I was thinking £7 a week”. There’s not a chance he’ll say no – it’s £3 cheaper than th bus and better in every way, he COULD run a second car, but as we all know, that ain’t cheap.
It’s 30 seconds of you pretending to have thick skin, either get your peace back, or more likely you get £350 a year, which if you put it in your piggy back would pay for – a flight to Geneva with your bike and a transfer to one of the resorts, a HT frame, s/h set of forks, wheelset who knows.