Upvote:3
Can anyone see any reason I would not be allowed entry for 6 weeks to travel, visit schools and see friends?
From the information you've given, no. I presume you are a British citizens and that you therefore received a 10-year multiple entry B-1/B-2 visa that is still valid.
You've been out of the country for over 200 days, so it's unlikely that you will be suspected of trying to live in the country. The reasons for your earlier periods of stay under the VWP and your visa may have an impact on this, however.
There's no reason you should have any trouble with a purpose of investigating graduate schools as a prospective student, nor for visiting friends or sightseeing.
You could of course have trouble on any of several other grounds you haven't raised. For example, you may be asked to show that you have means to support yourself for a 6-week trip. If you tell them that you're unemployed (for example, if they ask), you may need to show them how much money you have saved.
Further more, if we allow uninhibited speculation, the answer would certainly be "yes": it is not hard to think of a reason why you might be refused entry.
In general, however, the travel pattern you outline in the question will not disqualify you from admission for a six-week trip.