There are enough shops, garages and pubs to get water from, except at night when you'll be drinking less anyway.
Exactly. Thinking about the route, it's only the last stretch (Canonbie to Dalkeith) where there is a prolonged distance with possibly nowhere to buy water either on the route or by a very short detour off it.
Possibly also the Washingborugh to Thorne leg, as that will be Sunday evening (8am start) or early hours of Monday morning (2pm start).
From memory you'll be able to get stuff in:-
Cheshunt (control), Hertford/Bengeo (shops+petrol stations), Gamlingay (control + shops), St Neots (lots of shops), Kimbolton (shops), garage on the A47 near Wansford, Thurlby (control), Bourne (minor detour), Sleaford, Washingborough (control).
For the Southbound leg between Thorne and Lincoln: Thorne, Gainsborough (or detour to Rosies cafe), Lincoln (lots), Washingborough (control).
For the more northern bits there's Thirsk, Middleton Tyas (control), Barnard Castle, possibly something in Middleton-In-Teesdale, Langdon Beck (Youth Hostel), Alston (control+shops), Brampton (shops), Longtown (shops), Canonbie (control).
For just water stops you can always wander into a pub, they're usually always happy to top up water bottles although it's polite to ask if it's necessary to buy something (like a packet of crisps rather than a pint).
I'll have more info in a couple of weeks when I've done the northbound half.
Personally I only have one full 750ml bidon on the bike. The other bottle is usually empty. If I'm on a long stretch I'll fill up both, more often I just drink a litre of water or so whilst I'm at the control or shop/garage stop. 3.5kg is a lot of weight to add to the bike.