Early jump tech is MASSIVE. It will take about 1/3 the ship's mass for just the jump engine. It is very hard to build a decent warship with early jump tech. So that's why there are Jump Tenders.
And yes, the ship cannot transit anything larger than itself, even if the jump engine is rated higher. So in the case of battle fleet tenders, fill out the remaining space with fuel and magazines. Make it a dual/triple role ship, Jump Tender/Collier/Tanker. Just remember to check the appropriate boxes, otherwise it won't act like it.