I've done some 'Weir' fishing in the past although mainly on wiers somewhat bigger than the one in your pic, (such as those found on the upper Thames) and most need to be fished in a slightly different way, mainly for reasons of access. It can be a lovely way to fish but expensive in lost tackle if, for example casting into the water immediately below the sill, although many chose to fish this way by sitting downstream and casting into this area.
Your weir is quite gentle as weirs go (having a minimal change in level) but it still produces 'white water' after a fashion and a place where good fish gather, even very close to the sill...In fact I recall a well known angler hoiking out an 11lb carp from such an area on a weirpool at Cookham, Berks some years ago using a form of upstream ledgering with a slack line !
As Peter says, you need to do a bit of casting around to get an idea of water depth, but in the areabelow the sill I would (a) do as I've suggested above and fish upstream toward the sill if the bottom is okay, (b) fish various distances downstream from the sill where the water calms down, with either float, trotted if you have depth, or light ledger if not (c) if the water coming over the sill produces 'slacks' or 'eddies' (below the sill and close to the bank) then a float trotted in these area can work, again if you have some depth, or even a freelined bait such a worms or meat dropped into the 'slack' areas always worth a go........
Personally I think weir fishing, possibly more than most ways of fishing, needs thinking outside the box, and unconventional methods such as freelining etc can, and have, produced really good fish such as chub, perch and barbel BUT you do need to work at it and try different methods and areas - more a 'roving' type of fishing perhaps.....even trying for roach (say) 50 yds downstream where bits of food may well have gathered in slower water...
Oh, and don't forget the area immediately above the weir which although tending to be on the shallow side can hold good roach........................light ledger with flake and a feeder can be good
To summarize; From your pic you look to have loads of options available to you, from fast water to slow, from white water to slacks, and how you get the best from them is really down to how much effort (and time!) you're prepared to put in.........like all form of fishing !!
ps Watching the water, walking the banks in the evening or early morning and asking around, may well turn out to be time well spent ..
Good luck !!
ps You may well get some clearer answers if you could state what sort of fish you're after and what you might expect to catch - big barbell, chub, roach?...do you have any idea of what can be caught? Have you talked to the local tackle shops?
The 'private fishing' sign in your pic suggests good fishing BUT can be deceiving !!!