by way of introduction, I'm a 250lb internist with hypertension, on an ACEI, so I'm definitely sympathetic to your situation.
A few things-
1). Your bp is high enough to be concerning. With a family history of cardiovascular disease, and a higher BMI, you really should stay on top of your LDL, HDL (bad and good cholesterol), and make sure you aren't heading towards diabetes.
2). People with some size on them (BMI>30) who are in good shape (able to exercise to 10 mets) do about as well as smaller folks- this week's Archives of Internal Medicine has a nice study demonstrating this. Keep up with the cardio and lifting.
3). 'Lifestyle' modifications are an excellent suggestion, but your bp is high enough to go straight to pharmacologic intervention. You are unlikely to control your blood pressure with 'lifestyle' changes alone.
4). Salt restriction will lower your blood pressure if you're salt-sensitive. You can check this by letting your bp stabilize on your drug for a month or so, then restricting your salt intake to <3g/day, and checking daily bp at roughly the same time each day.
5). Cardiovascular exercise has a nice bp lowering effect.
6). Fish oil in 4-6gm/day dosing can lower bp by 8-12mmHG, though be aware that fish oil can raise both HDL and LDL (HDL up is good, LDL up is supposedly bad, but in this case some posit that this elevation may be due to a less harmful subtype of LDL).
7). 100gm dark chocolate a day is good for bp lowering effect similar to fish oil, and may have some nice antioxidant properties.
8). Low glycemic index diets have been associated with better blood pressure control.
9). ACEIs are excellent drugs. They are generally well tolerated (and if you think there's a problem, try another within the same class, unless your problem's cough, then switch to an ARB). They prevent progression of kidney disease and help regress pathologic thickening of the heart. While not without risks, there's a big upside to these drugs (they may also reduce risk of stroke in certain populations, and atrial fibrillation).
10). ACEIs inhibit one branch of the kidney's ability to autoregulate its internal hemodynamics. NSAIDS (naprosyn, ibuprophen, toradol, etc)inhibit the other branch. Don't take NSAIDS if you're on an ACEI; use acetominophen instead.
11). Stay hydrated when you train- volume depletion +ACEI can be a bit rough on the kidneys too.
12). The answer to your original question- you should feel fine, if not even better while training with your blood pressure controlled. ACEIs are not notorious for causing fatigue.
Hope this helps,